Showing 1–50 of 79 results for author: Reis, F

Non-monotonic roughness evolution in film growth on weakly interacting substrates

Authors: Dmitry Lapkin, Ismael S. S. Carrasco, Catherine Cruz Luukkonen, Oleg Konovalov, Alexander Hinderhofer, Frank Schreiber, Fábio D. A. Aarão Reis, Martin Oettel

Abstract: Thin film deposition on weakly interacting substrates exhibits a unique growth mode characterized by initially strong island formation and rapidly increasing roughness, which reaches a maximum and subsequently decreases as the film returns to a smooth morphology. Here we show this rough-to-smooth growth mode experimentally for two molecular systems with substantially different geometries, namely,… ▽ More Thin film deposition on weakly interacting substrates exhibits a unique growth mode characterized by initially strong island formation and rapidly increasing roughness, which reaches a maximum and subsequently decreases as the film returns to a smooth morphology. Here we show this rough-to-smooth growth mode experimentally for two molecular systems with substantially different geometries, namely, the effectively spherical buckminsterfullerene (C$_{60}$) and the disk-like 1,4,5,8,9,11-hexaazatriphenylenehexacarbonitrile (HATCN). This growth mode is explained by a geometrical model that captures the basic mechanisms of multilayer island growth, island coalescence, and formation of a continuous film. Additionally, kinetic Monte Carlo simulations with minimal ingredients demonstrate that this mode generally occurs for weakly interacting substrates, providing quantitative estimates of parameters that characterize adsorbate-adsorbate and adsorbate-substrate interactions. Both the model and simulations accurately describe the experimental data and highlight the generic nature of the phenomenon, independently of the details of the interactions and the molecular flux, which opens up a path for controlling nanoscale film roughness. △ Less

Submitted 24 January, 2026; originally announced January 2026.

Comments: Accepted to Physical Review Letters

Flat bands in ultra-wide gap two-dimensional germanium dioxide

Authors: Rafael Franco Ribeiro Reis, Gabriel Elyas Gama Araujo, Danilo Kuritza, Alexandre Cavalheiro Dias, Andreia Luisa da Rosa, Renato Borges Pontes

Abstract: We employ first principles density-functional theory (DFT) and the Bethe-Salpeter equation (BSE) in the framework of tight-binding based maximally localized Wannier functions (MLWF-TB) model to investigate the electronic and optical properties of free-standing two-dimensional (2D) germanium dioxide phases. All investigated 2D GeO2 polymorphs exhibit ultra-wide band gaps and strong excitonic effect… ▽ More We employ first principles density-functional theory (DFT) and the Bethe-Salpeter equation (BSE) in the framework of tight-binding based maximally localized Wannier functions (MLWF-TB) model to investigate the electronic and optical properties of free-standing two-dimensional (2D) germanium dioxide phases. All investigated 2D GeO2 polymorphs exhibit ultra-wide band gaps and strong excitonic effects, with flat O-p-derived valence bands tunable under strain. These features allow the design of flat band materials with ultra large electronic gaps in low-dimensional systems, making these materials promising for devices operation at higher voltages and temperatures than conventional semiconductor materials. △ Less

Submitted 28 October, 2025; originally announced October 2025.

Island formation in heteroepitaxial growth

Authors: Frederik Munko, Catherine Cruz Luukkonen, Ismael S. S. Carrasco, Fábio D. A. Aarão Reis, Martin Oettel

Abstract: Island formation in strain-free heteroepitaxial deposition of thin films is analyzed using kinetic Monte Carlo simulations of two minimal lattice models and scaling approaches. The transition from layer-by-layer (LBL) to island (ISL) growth is driven by a weaker binding strength of the substrate which, in the kinetic model, is equivalent to an increased diffusivity of particles on the substrate co… ▽ More Island formation in strain-free heteroepitaxial deposition of thin films is analyzed using kinetic Monte Carlo simulations of two minimal lattice models and scaling approaches. The transition from layer-by-layer (LBL) to island (ISL) growth is driven by a weaker binding strength of the substrate which, in the kinetic model, is equivalent to an increased diffusivity of particles on the substrate compared to particles on the film. The LBL-ISL transition region is characterized by particle fluxes between layers 1 and 2 significantly exceeding the net flux between them, which sets a quasi-equilibrium condition. Deposition on top of monolayer islands weakly contributes to second layer nucleation, in contrast with the homoepitaxial growth case. A thermodynamic approach for compact islands with one or two layers predicts the minimum size in which the second layer is stable. When this is linked to scaling expressions for submonolayer island deposition, the dependence of the ISL-LBL transition point on the kinetic parameters qualitatively matches the simulation results, with quantitative agreement in some parameter ranges. The transition occurs in the equilibrium regime of partial wetting and the convergence of the transition point upon reducing the deposition rate is very slow and practically unattainable in experiments. △ Less

Submitted 14 November, 2024; originally announced November 2024.

Effective medium theory for the electrical conductance of random resistor networks which mimic crack-template-based transparent conductive films

Authors: Yuri Yu. Tarasevich, Irina V. Vodolazskaya, Andrei V. Eserkepov, Fábio D. A. Aarão Reis

Abstract: We studied random resistor networks produced with regular structure and random distribution of edge conductances. These networks are intended to mimic crack-template-based transparent conductive films as well some random networks produced using nano-imprinting technology. Applying an effective medium theory, we found out that the electrical conductance of such networks is… ▽ More We studied random resistor networks produced with regular structure and random distribution of edge conductances. These networks are intended to mimic crack-template-based transparent conductive films as well some random networks produced using nano-imprinting technology. Applying an effective medium theory, we found out that the electrical conductance of such networks is $\approx 0.5852 \sqrt{n_E}$, where $n_E$ is the number density of conductive edges. This dependence is in agreement with numerical calculations in Voronoi networks, although the effective conductances are approximately 15\% larger. △ Less

Submitted 21 June, 2024; v1 submitted 15 March, 2024; originally announced March 2024.

Comments: 7 pages, 4 figures, 1 table, 68 references

Observation of room temperature excitons in an atomically thin topological insulator

Authors: Marcin Syperek, Raul Stühler, Armando Consiglio, Paweł Holewa, Paweł Wyborski, Łukasz Dusanowski, Felix Reis, Sven Höfling, Ronny Thomale, Werner Hanke, Ralph Claessen, Domenico Di Sante, Christian Schneider

Abstract: Optical spectroscopy of ultimately thin materials has significantly enhanced our understanding of collective excitations in low-dimensional semiconductors. This is particularly reflected by the rich physics of excitons in atomically thin crystals which uniquely arises from the interplay of strong Coulomb correlation, spin-orbit coupling (SOC), and lattice geometry. Here we extend the field by repo… ▽ More Optical spectroscopy of ultimately thin materials has significantly enhanced our understanding of collective excitations in low-dimensional semiconductors. This is particularly reflected by the rich physics of excitons in atomically thin crystals which uniquely arises from the interplay of strong Coulomb correlation, spin-orbit coupling (SOC), and lattice geometry. Here we extend the field by reporting the observation of room temperature excitons in a material of non-trivial global topology. We study the fundamental optical excitation spectrum of a single layer of bismuth atoms epitaxially grown on a SiC substrate (hereafter bismuthene or Bi/SiC) which has been established as a large-gap, two-dimensional (2D) quantum spin Hall (QSH) insulator. Strongly developed optical resonances are observed to emerge around the direct gap at the K and K' points of the Brillouin zone, indicating the formation of bound excitons with considerable oscillator strength. These experimental findings are corroborated, concerning both the character of the excitonic resonances as well as their energy scale, by ab-initio \emph{GW} and Bethe-Salpeter equation calculations, confirming strong Coulomb interaction effects in these optical excitations. Our observations provide the first evidence of excitons in a 2D QSH insulator at room temperature, with excitonic and topological physics deriving from the very same electronic structure. △ Less

Submitted 27 March, 2023; v1 submitted 13 September, 2022; originally announced September 2022.

Energy levels for $\mathcal{PT}$-symmetric deformation of the Mathieu equation

Authors: E. Cavalcanti, N. M. Alvarenga, F. Reis, J. R. Mahon, C. A. Linhares, J. A. Lourenço

Abstract: We propose a non-Hermitian deformation of the Mathieu equation that preserves $\mathcal{PT}$ symmetry and study its spectrum and the transition from $\mathcal{PT}$-unbroken to $\mathcal{PT}$-broken phases. We show that our model not only reproduces behaviors expected by the literature but also indicates the existence of a richer structure for the spectrum. We also discuss the influence of the boun… ▽ More We propose a non-Hermitian deformation of the Mathieu equation that preserves $\mathcal{PT}$ symmetry and study its spectrum and the transition from $\mathcal{PT}$-unbroken to $\mathcal{PT}$-broken phases. We show that our model not only reproduces behaviors expected by the literature but also indicates the existence of a richer structure for the spectrum. We also discuss the influence of the boundary condition and the model parameters in the exceptional line that marks the $\mathcal{PT}$ breaking. △ Less

Submitted 28 April, 2022; originally announced April 2022.

Interface collisions with diffusive mass transport

Authors: Bastien Marguet, F. D. A. Aarão Reis, Olivier Pierre-Louis

Abstract: We report on a linear Langevin model that describes the evolution of the roughness of two interfaces that move towards each other and are coupled by a diffusion field. This model aims at describing the closing of the gap between two two-dimensional material domains during growth, and the subsequent formation of a rough grain boundary. We assume that deposition occurs in the gap between the two dom… ▽ More We report on a linear Langevin model that describes the evolution of the roughness of two interfaces that move towards each other and are coupled by a diffusion field. This model aims at describing the closing of the gap between two two-dimensional material domains during growth, and the subsequent formation of a rough grain boundary. We assume that deposition occurs in the gap between the two domains and that the growth units diffuse and may attach to the edges of the domains. These units can also detach from edges, diffuse, and re-attach elsewhere. For slow growth, the edge roughness increases monotonously and then saturates at some equilibrium value. For fast growth, the roughness exhibits a maximum just before the collision between the two interfaces, which is followed by a minimum. The peak of the roughness can be dominated by statistical fluctuations or by edge instabilities. A phase diagram with three regimes is obtained: slow growth without peak, peak dominated by statistical fluctuations, and peak dominated by instabilities. These results reproduce the main features observed in Kinetic Monte Carlo simulations. △ Less

Submitted 12 April, 2022; originally announced April 2022.

Comments: 18 pages, 16 Figures

Growth at high substrate coverage can decrease the grain boundary roughness of 2D materials

Authors: Fabio D. A. Aarão Reis, Bastien Marguet, Olivier Pierre-Louis

Abstract: Grain boundary roughness can affect electronic and mechanical properties of two-dimensional materials. This roughness depends crucially on the growth process by which the two-dimensional material is formed. To investigate the key mechanisms that govern the roughness, we have performed kinetic Monte Carlo simulations of a simple model that includes particle attachment, detachment, and diffusion. We… ▽ More Grain boundary roughness can affect electronic and mechanical properties of two-dimensional materials. This roughness depends crucially on the growth process by which the two-dimensional material is formed. To investigate the key mechanisms that govern the roughness, we have performed kinetic Monte Carlo simulations of a simple model that includes particle attachment, detachment, and diffusion. We have studied the closure of the gap between two flakes during growth, and the subsequent formation of the grain boundary (GB) for a broad range of model parameters. The well known near-equilibrium (attachment-limited) and unstable (diffusion-limited) growth regimes are identified, but we also observe a third regime when the precursor flux is sufficiently high to fully cover the gap between the edges. This high coverage regime forms GBs with spatially uncorrelated roughness, which quickly relax to smoother configurations. Extrapolating the numerical results (with support from a theoretical approach) to edge lengths and gap widths of some micrometers, we confirm the advantage of this regime to produce GBs with minimal roughness faster than near-equilibrium conditions. This suggests an unexpected route towards efficient growth of two-dimensional materials with smooth GBs. △ Less

Submitted 4 April, 2022; originally announced April 2022.

Lifting topological protection in a quantum spin Hall insulator by edge coupling

Authors: Raul Stühler, André Kowalewski, Felix Reis, Dimitri Jungblut, Fernando Dominguez, Benedikt Scharf, Gang Li, Jörg Schäfer, Ewelina M. Hankiewicz, Ralph Claessen

Abstract: The scientific interest in two-dimensional topological insulators (2D TIs) is currently shifting from a more fundamental perspective to the exploration and design of novel functionalities. Key concepts for the use of 2D TIs in spintronics are based on the topological protection and spin-momentum locking of their helical edge states. In this study we present experimental evidence that topological p… ▽ More The scientific interest in two-dimensional topological insulators (2D TIs) is currently shifting from a more fundamental perspective to the exploration and design of novel functionalities. Key concepts for the use of 2D TIs in spintronics are based on the topological protection and spin-momentum locking of their helical edge states. In this study we present experimental evidence that topological protection can be (partially) lifted by pairwise coupling of 2D TI edges in close proximity. Using direct wave function mapping via scanning tunneling microscopy/spectroscopy (STM/STS) we compare isolated and coupled topological edges in the 2D TI bismuthene. The latter situation is realized by natural lattice line defects and reveals distinct quasi-particle interference (QPI) patterns, identified as electronic Fabry-Pérot resonator modes. In contrast, free edges show no sign of any single-particle backscattering. These results pave the way for novel device concepts based on active control of topological protection through inter-edge hybridization for, e.g., electronic Fabry-Pérot interferometry. △ Less

Submitted 8 November, 2021; originally announced November 2021.

Effects of the growth kinetics on solute diffusion in porous films

Authors: Gabriela B. Correa, Renan A. L. Almeida, Fabio D. A. Aarao Reis

Abstract: For the development of porous materials with improved transport properties, a key missing ingredient is to determine the relations between growth kinetics, structure, and transport parameters. Here, we address these relations by studying solute diffusion through three-dimensional porous films produced by simple deposition models with controlled thickness and porosity. We simulate growing films wit… ▽ More For the development of porous materials with improved transport properties, a key missing ingredient is to determine the relations between growth kinetics, structure, and transport parameters. Here, we address these relations by studying solute diffusion through three-dimensional porous films produced by simple deposition models with controlled thickness and porosity. We simulate growing films with competitive aggregation rules that incorporate lateral aggregation (relative rate proportional to $p$), which leads to pore formation, and surface relaxation ($1-p$) that favors compaction. By connecting a solute source at the basis and a drain at the top outer surface of the films, we extract the effective diffusion coefficients from steady-state simulations. We find that for a given film thickness, the larger the $p$, the larger the effective porosity and diffusivity, but the smaller the tortuosity. Keeping constant growth conditions (i.e., same $p$), the increase of thickness always leads to an increase of effective porosity, but a nontrivial behavior in the diffusivity occurs: for $p\leq 0.7$, the diffusion coefficient is larger in thicker films; this is accompanied by a decrease of the tortuosity with the thickness, thus indicating that growth continuously improves pore structure for diffusion. Microscopically, such a result is associated with narrower distributions of local solute currents at higher points of films. Particularly for $p\geq 0.9$, in which film porosity is $\sim 0.65-0.7$, the tortuosity is between $1.3$ and $2$, increases with the thickness, and has maximal changes near $25\%$. Pairs of values of porosity and tortuosity that we obtain here, for the thickest films, agree with those experimentally measured in some porous electrodes. Noteworthy, the increase of film thickness is generally favorable for diffusion in their pores, and exceptions have small losses in tortuosity. △ Less

Submitted 13 March, 2024; v1 submitted 23 July, 2021; originally announced July 2021.

Comments: Main: 37 pages, 11 figures, 2 tables. Suppl. Mat.: 7 pages, 4 figures. Paper written by F. Reis

Journal ref: G. B. Correa, R. Almeida, F. D. A. A. Reis, J. Phys. Chem. C 124 (2020) 19101-19111

Roughness and Correlations in the Transition from Island to Film Growth: Simulations and Application to CdTe Deposition

Authors: Tung B. T. To, Renan A. L. Almeida, Sukarno O. Ferreira, Fábio D. A. Aarão Reis

Abstract: Using kinetic Monte Carlo simulations, we develop a framework to relate morphological properties and microscopic dynamics during island growth, coalescence, and initial formation of continuous heteroepitaxial films. The average island width is controlled by adatom mobility on the substrate. Subsequent evolution strongly depends on the Ehrlich-Schwöebel energy barrier $E_{ES}$ of the deposited mate… ▽ More Using kinetic Monte Carlo simulations, we develop a framework to relate morphological properties and microscopic dynamics during island growth, coalescence, and initial formation of continuous heteroepitaxial films. The average island width is controlled by adatom mobility on the substrate. Subsequent evolution strongly depends on the Ehrlich-Schwöebel energy barrier $E_{ES}$ of the deposited material. As $E_{ES}$ decreases, islands becomes taller and their coalescence is delayed. For small islands and large $E_{ES}$, the global roughness increases as $W\sim{\text{thickness}}^{1/2}$ and the local roughness increases at short scales (apparent anomalous scaling) before and after island coalescence. If the islands are wide, $W$ may have a plateau for large $E_{ES}$ and has a maximum for small $E_{ES}$ when the islands coalesce. This framework is applied to atomic-force microscopy data of the initial stages of CdTe deposition on Kapton: a maximum of $W$ during island coalescence indicates negligible ES barrier, consistently with scaling properties of much thicker films, and the diffusion coefficient ${10}^{-7}{\text{--}}{10}^{-5}{\text{cm}}^2/{\text s}$ on the Kapton surface at $150\,^{\circ}\mathrm{C}$ is estimated. Applications of the framework to other materials are suggested, in which the expected roles of ES barriers are highlighted. △ Less

Submitted 21 July, 2021; v1 submitted 21 May, 2021; originally announced May 2021.

Journal ref: Applied Surface Science 560 (2021) 149946

Time increasing rates of infiltration and reaction in porous media at the percolation thresholds

Authors: Ismael S. S. Carrasco, Fábio D. A. Aarão Reis

Abstract: The infiltration of a solute in a fractal porous medium is usually anomalous, but chemical reactions of the solute and that material may increase the porosity and affect the evolution of the infiltration. We study this problem in two- and three-dimensional lattices with randomly distributed porous sites at the critical percolation thresholds and with a border in contact with a reservoir of an aggr… ▽ More The infiltration of a solute in a fractal porous medium is usually anomalous, but chemical reactions of the solute and that material may increase the porosity and affect the evolution of the infiltration. We study this problem in two- and three-dimensional lattices with randomly distributed porous sites at the critical percolation thresholds and with a border in contact with a reservoir of an aggressive solute. The solute infiltrates that medium by diffusion and the reactions with the impermeable sites produce new porous sites with a probability $r$, which is proportional to the ratio of reaction and diffusion rates at the scale of a lattice site. Numerical simulations for $r\ll1$ show initial subdiffusive scaling and long time Fickean scaling of the infiltrated volumes or areas, but with an intermediate regime with time increasing rates of infiltration and reaction. The anomalous exponent of the initial regime agrees with a relation previously applied to infinitely ramified fractals. We develop a scaling approach that explains the subsequent time increase of the infiltration rate, the dependence of this rate on $r$, and the crossover to the Fickean regime. The exponents of the scaling relations depend on the fractal dimensions of the critical percolation clusters and on the dimensions of random walks in those clusters. The time increase of the reaction rate is also justified by that reasoning. As $r$ decreases, there is an increase in the number of time decades of the intermediate regime, which suggests that the time increasing rates are more likely to be observed is slowly reacting systems. △ Less

Submitted 23 February, 2021; originally announced February 2021.

Comments: 14 pages, 13 figures

Journal ref: Phys. Rev. E 103, 022138 - Published 22 February 2021

Statistics of adatom diffusion in a model of thin film growth

Authors: Edwin E. Mozo Luis, Ismael S. S. Carrasco, Thiago A. de Assis, Fábio D. A. Aarão Reis

Abstract: We study the statistics of the number of executed hops of adatoms at the surface of films grown with the Clarke-Vvedensky (CV) model in simple cubic lattices. The distributions of this number, $N$, are determined in films with average thicknesses close to $50$ and $100$ monolayers for a broad range of values of the diffusion-to-deposition ratio $R$ and of the probability $ε$ that lowers the diffus… ▽ More We study the statistics of the number of executed hops of adatoms at the surface of films grown with the Clarke-Vvedensky (CV) model in simple cubic lattices. The distributions of this number, $N$, are determined in films with average thicknesses close to $50$ and $100$ monolayers for a broad range of values of the diffusion-to-deposition ratio $R$ and of the probability $ε$ that lowers the diffusion coefficient for each lateral neighbor. The mobility of subsurface atoms and the energy barriers for crossing step edges are neglected. Simulations show that the adatoms execute uncorrelated diffusion during the time in which they move on the film surface. In a low temperature regime, typically with $Rε\lesssim 1$, the attachment to lateral neighbors is almost irreversible, the average number of hops scales as $\langle N\rangle \sim R^{0.38\pm 0.01}$, and the distribution of that number decays approximately as $\exp\left[-\left({N/\langle N\rangle}\right)^{0.80\pm 0.07}\right]$. Similar decay is observed in simulations of random walks in a plane with randomly distributed absorbing traps and the estimated relation between $\langle N\rangle$ and the density of terrace steps is similar to that observed in the trapping problem, which provides a conceptual explanation of that regime. As the temperature increases, $\langle N\rangle$ crosses over to another regime when $Rε^{3.0\pm 0.3}\sim 1$, which indicates high mobility of all adatoms at terrace borders. The distributions $P\left( N\right)$ change to simple exponential decays, due to the constant probability for an adatom to become immobile after being covered by a new deposited layer. At higher temperatures, the surfaces become very smooth and $\langle N\rangle \sim Rε^{1.85\pm 0.15}$, which is explained by an analogy with submonolayer growth. △ Less

Submitted 24 July, 2020; originally announced July 2020.

Journal ref: Physical Review E 102, 012805 (2020)

Thin film growth models with long surface diffusion lengths

Authors: Tung B. T. To, Vitor B. de Sousa, Fábio D. A. Aarão Reis

Abstract: In limited mobility (LM) models of thin film deposition, the final position of each atom or molecule is chosen according to a set of stochastic rules before the incidence of another atom or molecule. Here we investigate the possibility of a LM model to reproduce features of a more realistic approach that represents the interplay of collective adatom diffusion and the external flux. In the LM model… ▽ More In limited mobility (LM) models of thin film deposition, the final position of each atom or molecule is chosen according to a set of stochastic rules before the incidence of another atom or molecule. Here we investigate the possibility of a LM model to reproduce features of a more realistic approach that represents the interplay of collective adatom diffusion and the external flux. In the LM model introduced here, each adatom may execute $G$ hops to neighboring columns of the deposit, but a hop attempt from a site with $n$ lateral neighbors has probability $P^n$, with $P<1$. These rules resemble those of the Clarke-Vvedensky (CV) model without energy barriers at step edges, whose main parameters are the diffusion-to-deposition ratio $R$ on terraces and the detachment probability $ε$ per lateral neighbor. At short times, the roughness of the LM model can be written in terms of a scaling function of $G$ and $P$ and the growth exponent is consistent with the Villain-Lai-Das Sarma universality class. The evolution of the surface roughness and of the autocorrelation function of the CV model is reproduced with reasonable accuracy by the LM model with suitable choices of parameters. The increase of the parameters $G$ and $R$ of those models produces smoother film surfaces, while the increase of $P$ and $ε$ smoothen the terrace boundaries at short lengthscales. However, the detachment probabilities of the two models have very different effects on the surface roughness: in the LM model, for fixed $G$, the surface roughness increases as $P$ increases; in the CV model, the surface smoothens as $ε$ increases, for fixed $R$. This result is related to the non-Markovian nature of the LM model, since the diffusivity of an adatom depends on its history at the film surface and may be severely reduced after a detachment from a terrace step. △ Less

Submitted 8 May, 2020; v1 submitted 9 April, 2020; originally announced April 2020.

Comments: Preprint for a publication in Physica A

Journal ref: Physica A 511 (2018) 240-250

Domain formation in the deposition of thin films of two-component mixtures

Authors: Tung B. T. To, Fábio D. A. Aarão Reis

Abstract: We perform a kinetic Monte Carlo simulation study of a model of thin film deposition of a two-component mixture in which the activation energy for diffusion of an adatom is additive over its nearest neighbors and in which the interactions between adatoms of the same species are stronger than those between adatoms of different species. The film morphology is investigated for broad ranges of values… ▽ More We perform a kinetic Monte Carlo simulation study of a model of thin film deposition of a two-component mixture in which the activation energy for diffusion of an adatom is additive over its nearest neighbors and in which the interactions between adatoms of the same species are stronger than those between adatoms of different species. The film morphology is investigated for broad ranges of values of the ratios between terrace diffusivity and atomic flux, of the probabilities of detachment from lateral neighbors, and of probabilities of crossing terrace edges. First, we consider a symmetric case in which the interactions of adatoms of the same species are the same for the two components. For low and intermediate temperatures, we show the formation of narrow domains, whose widths are $3$-$30$ lattice constants, which meander in the layers parallel to the substrate, and are connected through very long distances. The domain width depends on the diffusivity-flux ratio of the same species, but it is weakly affected by interactions of different species, so rough estimates of that width can be obtained by using tabulated properties of films with a single component. At high temperatures, the separation of domains is enhanced, but their long distance connectivity is lost, which shows that the formation of the long meandering domains is restricted to a certain range of temperature and flux. Similar morphological features are obtained when the intra-species interactions are different and the adatom diffusion coefficients on terraces of the same species differ up to two orders of magnitude. An approximate scaling relation for the domain width is obtained, but the species with the largest mobility constrains the temperature range in which the long connected domains are found. △ Less

Submitted 8 May, 2020; v1 submitted 9 April, 2020; originally announced April 2020.

Comments: Preprint accepted for publication by Journal of Alloys and Compounds

Journal ref: Journal of Alloys and Compounds 835 (2020) 155093(1-14)

Tailoring the topological surface state in ultrathin $α$-Sn (111) films

Authors: Victor A. Rogalev, Felix Reis, Florian Adler, Maximilian Bauernfeind, Jonas Erhardt, André Kowalewski, Markus R. Scholz, Lenart Dudy, Liam B. Duffy, Thorsten Hesjedal, Moritz Hoesch, Gustav Bihlmayer, Jörg Schäfer, Ralph Claessen

Abstract: We report on the electronic structure of $α$-Sn films in the very low thickness regime grown on InSb(111)A. High-resolution low photon energies angle-resolved photoemission (ARPES) allows for the direct observation of the linearly dispersing 2D topological surface states (TSSs) that exist between the second valence band and the conduction band. The Dirac point of this TSS was found to be 200meV be… ▽ More We report on the electronic structure of $α$-Sn films in the very low thickness regime grown on InSb(111)A. High-resolution low photon energies angle-resolved photoemission (ARPES) allows for the direct observation of the linearly dispersing 2D topological surface states (TSSs) that exist between the second valence band and the conduction band. The Dirac point of this TSS was found to be 200meV below the Fermi level in 10-nm-thick $α$-Sn films, which enables the observation of the hybridization gap opening at the Dirac point of the TSS for thinner films. The crossover to a quasi-2D electronic structure is accompanied by a full gap opening at the Brillouin zone center, in agreement with our density functional theory calculations. We further identify the thickness regime of $α$-Sn films where the hybridization gap in TSS coexists with the topologically non-trivial electronic structure and one can expect the presence of a 1D helical edge states. △ Less

Submitted 6 December, 2019; v1 submitted 24 October, 2019; originally announced October 2019.

Comments: 7 pages, 5 figures, 1 table

Journal ref: Phys. Rev. B 100, 245144 (2019)

Models of infiltration into homogeneous and fractal porous media with localized sources

Authors: Fabio D. A. Aarao Reis, Vaughan R. Voller

Abstract: We study a random walk infiltration (RWI) model, in homogeneous and in fractal media, with localized sources at their boundaries. The particles released at a source, which is maintained at a constant density, execute unbiased random walks over a lattice; it represents solute infiltration by diffusion into a medium in contact with a reservoir. A scaling approach shows that the infiltrated length, a… ▽ More We study a random walk infiltration (RWI) model, in homogeneous and in fractal media, with localized sources at their boundaries. The particles released at a source, which is maintained at a constant density, execute unbiased random walks over a lattice; it represents solute infiltration by diffusion into a medium in contact with a reservoir. A scaling approach shows that the infiltrated length, area, or volume evolves in time as the number of distinct sites visited by a single random walker in the same medium. This is consistent with simulations of the lattice model and exact and numerical solutions of the corresponding diffusion equation. In a Sierpinski carpet, the infiltrated area is expected to evolve as t^{D_F/D_W} (Alexander-Orbach relation), where D_F is the fractal dimension of the medium and D_W is the random walk dimension; the numerical integration of the diffusion equation supports this relation and improves results of lattice random walk simulations. In a Menger sponge in which D_F>D_W (a fractal with a dimension close to 3), a linear time increase of the infiltrated volume is predicted and confirmed numerically. Thus, no evidence of fractality can be observed in infiltrated volumes or masses in media where random walks are not recurrent, although the tracer diffusion is anomalous. We compare our results with a fluid infiltration model in which the pressure head is constant at the source and the front displacement is driven by the local gradient of that head. Exact or numerical solutions in two and three dimensions and in a carpet show that this type of fluid infiltration is in the same universality class of RWI, with an equivalence between the head and the particle concentration. These results set a relation between different infiltration processes with localized sources and the recurrence properties of random walks in the same media. △ Less

Submitted 10 April, 2019; originally announced April 2019.

Comments: 11 pages, 12 figures included

Journal ref: Phys. Rev. E 99, 042111 (2019)

Non-trivial topological valence bands of common diamond and zinc-blende semiconductors

Authors: Tomáš Rauch, Victor A. Rogalev, Maximilian Bauernfeind, Julian Maklar, Felix Reis, Florian Adler, Simon Moser, Johannes Weis, Tien-Lin Lee, Pardeep K. Thakur, Jörg Schäfer, Ralph Claessen, Jürgen Henk, Ingrid Mertig

Abstract: The diamond and zinc-blende semiconductors are well-known and have been widely studied for decades. Yet, their electronic structure still surprises with unexpected topological properties of the valence bands. In this joint theoretical and experimental investigation we demonstrate for the benchmark compounds InSb and GaAs that the electronic structure features topological surface states below the F… ▽ More The diamond and zinc-blende semiconductors are well-known and have been widely studied for decades. Yet, their electronic structure still surprises with unexpected topological properties of the valence bands. In this joint theoretical and experimental investigation we demonstrate for the benchmark compounds InSb and GaAs that the electronic structure features topological surface states below the Fermi energy. Our parity analysis shows that the spin-orbit split-off band near the valence band maximum exhibits a strong topologically non-trivial behavior characterized by the $\mathcal{Z}_2$ invariants $(1;000)$. The non-trivial character emerges instantaneously with non-zero spin-orbit coupling, in contrast to the conventional topological phase transition mechanism. \textit{Ab initio}-based tight-binding calculations resolve topological surface states in the occupied electronic structure of InSb and GaAs, further confirmed experimentally by soft X-ray angle-resolved photoemission from both materials. Our findings are valid for all other materials whose valence bands are adiabatically linked to those of InSb, i.e., many diamond and zinc-blende semiconductors, as well as other related materials, such as half-Heusler compounds. △ Less

Submitted 10 April, 2019; originally announced April 2019.

Journal ref: Phys. Rev. Materials 3, 064203 (2019)

Crossover from compact to branched films in electrodeposition with surface diffusion

Authors: F. D. A. Aarão Reis, Dung di Caprio, Abdelhafed Taleb

Abstract: We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute act… ▽ More We study a model for thin film electrodeposition in which instability development by preferential adsorption and reduction of cations at surface peaks competes with surface relaxation by diffusion of the adsorbates. The model considers cations moving in a supported electrolyte, adsorption and reduction when they reach the film surface, and consequent production of mobile particles that execute activated surface diffusion, which is represented by a sequence of random hops to neighboring lattice sites with a maximum of G hop attempts (G>>1), a detachment probability epsilon<1 per neighboring particle, and a no-desorption condition. Computer simulations show the formation of a compact wetting layer followed by the growth of branched deposits. The maximal thickness z_c of that layer increases with G, but is weakly affected by epsilon. A scaling approach describes the crossover from smooth film growth to unstable growth and predicts z_c ~ G^gamma, with gamma = 1/[2(1-nu)] = 0.43, where nu=0.30 is the inverse of the dynamical exponent of the Villain-Lai-Das Sarma equation that describes the initial roughening. Using previous results for related deposition models, the thickness z_c can be predicted as a function of an activation energy for terrace surface diffusion and the temperature, and the small effects of the parameter epsilon are justified. These predictions are confirmed by the numerical results with good accuracy. We discuss possible applications, with a particular focus on the growth of multifuncional structures with stacking layers of different porosity. △ Less

Submitted 3 March, 2019; originally announced March 2019.

Comments: Two-column format with 12 pages, 7 figures included

Journal ref: Phys. Rev. E 96, 022805 (2017)

Interface Collisions

Authors: Fabio D. A. Aarao Reis, Olivier Pierre-Louis

Abstract: We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form rough domain boundaries, which defines collision interfaces in time and space. We show that statistical properties of such interfaces depend on the kinetics of t… ▽ More We provide a theoretical framework to analyze the properties of frontal collisions of two growing interfaces considering different short range interactions between them. Due to their roughness, the collision events spread in time and form rough domain boundaries, which defines collision interfaces in time and space. We show that statistical properties of such interfaces depend on the kinetics of the growing interfaces before collision, but are independent of the details of their interaction and of their fluctuations during the collision. Those properties exhibit dynamic scaling with exponents related to the growth kinetics, but their distributions may be non-universal. These results are supported by simulations of lattice models with irreversible dynamics and local interactions. Relations to first passage processes are discussed and a possible application to grain boundary formation in two-dimensional materials is suggested. △ Less

Submitted 3 February, 2019; originally announced February 2019.

Comments: Paper with 12 pages and 2 figures; supplemental material with 4 pages and 3 figures

Journal ref: Phys. Rev. E 97, 040801(R) (2018)

Tomonaga-Luttinger liquid in the edge channels of a quantum spin Hall insulator

Authors: R. Stühler, F. Reis, T. Müller, T. Helbig, T. Schwemmer, R. Thomale, J. Schäfer, R. Claessen

Abstract: Topological quantum matter is characterized by non-trivial global invariants of the bulk which induce gapless electronic states at its boundaries. A case in point are two-dimensional topological insulators (2D-TI) which host one-dimensional (1D) conducting helical edge states protected by time-reversal symmetry (TRS) against single-particle backscattering (SPB). However, as two-particle scattering… ▽ More Topological quantum matter is characterized by non-trivial global invariants of the bulk which induce gapless electronic states at its boundaries. A case in point are two-dimensional topological insulators (2D-TI) which host one-dimensional (1D) conducting helical edge states protected by time-reversal symmetry (TRS) against single-particle backscattering (SPB). However, as two-particle scattering is not forbidden by TRS [1], the existence of electronic interactions at the edge and their notoriously strong impact on 1D states may lead to an intriguing interplay between topology and electronic correlations. In particular, it is directly relevant to the question in which parameter regime the quantum spin Hall effect (QSHE) expected for 2D-TIs becomes obscured by these correlation effects that prevail at low temperatures [2]. Here we study the problem on bismuthene on SiC(0001) which has recently been synthesized and proposed to be a candidate material for a room-temperature QSHE [3]. By utilizing the accessibility of this monolayer-substrate system on atomic length scales by scanning tunneling microscopy/spectroscopy (STM/STS) we observe metallic edge channels which display 1D electronic correlation effects. Specifically, we prove the correspondence with a Tomonaga-Luttinger liquid (TLL), and, based on the observed universal scaling of the differential tunneling conductivity (dI/dV), we derive a TLL parameter K reflecting intermediate electronic interaction strength in the edge states of bismuthene. This establishes the first spectroscopic identification of 1D electronic correlation effects in the topological edge states of a 2D-TI. △ Less

Submitted 18 January, 2019; originally announced January 2019.

A new paradigm for the quantum spin Hall effect at high temperatures

Authors: Gang Li, Werner Hanke, Ewelina M. Hankiewicz, Felix Reis, Joerg Schaefer, Ralph Claessen, Congjun Wu, Ronny Thomale

Abstract: The quantum spin Hall effect (QSHE) has formed the seed for contemporary research on topological quantum states of matter. Since its discovery in HgTe/CdTe quantum wells and AlGaAs/GaAs heterostructures, all such systems have so far been suffering from extremely low operating temperatures, rendering any technological application out of reach. We formulate a theoretical paradigm to accomplish the h… ▽ More The quantum spin Hall effect (QSHE) has formed the seed for contemporary research on topological quantum states of matter. Since its discovery in HgTe/CdTe quantum wells and AlGaAs/GaAs heterostructures, all such systems have so far been suffering from extremely low operating temperatures, rendering any technological application out of reach. We formulate a theoretical paradigm to accomplish the high temperature QSHE in monolayer-substrate heterostructures. Specifically, we explicate our proposal for hexagonal compounds formed by monolayers of heavy group-V elements (As, Sb, Bi) on a SiC substrate. We show how orbital filtering due to substrate hybridization, a tailored multi-orbital density of states at low energies, and large spin-orbit coupling can conspire to yield QSH states with bulk gaps of several hundreds of meV. Combined with the successful realization of Bi/SiC (0001), with a measured bulk gap of 800 meV reported previously [Reis et al., 10.1126/science.aai8142 (2017)], our paradigm elevates the QSHE from an intricate quantum phenomenon at low temperatures to a scalable effect amenable to device design and engineering. △ Less

Submitted 25 July, 2018; originally announced July 2018.

Comments: 16 pages, 9 figures

Journal ref: Phys. Rev. B 98, 165146 (2018)

The topological surface state of $α$-Sn on InSb(001) as studied by photoemission

Authors: M. R. Scholz, V. A. Rogalev, L. Dudy, F. Reis, F. Adler, J. Aulbach, L. J. Collins-McIntyre, L. B. Duffy, H. F. Yang, Y. L. Chen, T. Hesjedal, Z. K. Liu, M. Hoesch, S. Muff, J. H. Dil, J. Schäfer, R. Claessen

Abstract: We report on the electronic structure of the elemental topological semimetal $α$-Sn on InSb(001). High-resolution angle-resolved photoemission data allow to observe the topological surface state (TSS) that is degenerate with the bulk band structure and show that the former is unaffected by different surface reconstructions. An unintentional $p$-type doping of the as-grown films was compensated by… ▽ More We report on the electronic structure of the elemental topological semimetal $α$-Sn on InSb(001). High-resolution angle-resolved photoemission data allow to observe the topological surface state (TSS) that is degenerate with the bulk band structure and show that the former is unaffected by different surface reconstructions. An unintentional $p$-type doping of the as-grown films was compensated by deposition of potassium or tellurium after the growth, thereby shifting the Dirac point of the surface state below the Fermi level. We show that, while having the potential to break time-reversal symmetry, iron impurities with a coverage of up to 0.25 monolayers do not have any further impact on the surface state beyond that of K or Te. Furthermore, we have measured the spin-momentum locking of electrons from the TSS by means of spin-resolved photoemission. Our results show that the spin vector lies fully in-plane, but it also has a finite radial component. Finally, we analyze the decay of photoholes introduced in the photoemission process, and by this gain insight into the many-body interactions in the system. Surprisingly, we extract quasiparticle lifetimes comparable to other topological materials where the TSS is located within a bulk band gap. We argue that the main decay of photoholes is caused by intraband scattering, while scattering into bulk states is suppressed due to different orbital symmetries of bulk and surface states. △ Less

Submitted 29 November, 2017; originally announced November 2017.

Journal ref: Phys. Rev. B 97, 075101 (2018)

Effects of porosity in a model of corrosion and passive layer growth

Authors: F. D. A. Aarão Reis

Abstract: We introduce a stochastic lattice model to investigate the effects of pore formation in a passive layer grown with products of metal corrosion. It considers that an anionic species diffuses across that layer and reacts at the corrosion front (metal-oxide interface), producing a random distribution of compact regions and large pores, respectively represented by O (oxide) and P (pore) sites. O sites… ▽ More We introduce a stochastic lattice model to investigate the effects of pore formation in a passive layer grown with products of metal corrosion. It considers that an anionic species diffuses across that layer and reacts at the corrosion front (metal-oxide interface), producing a random distribution of compact regions and large pores, respectively represented by O (oxide) and P (pore) sites. O sites are assumed to have very small pores, so that the fraction $Φ$ of P sites is an estimate of the porosity, and the ratio between anion diffusion coefficients in those regions is $D_{\text r}<1$. Simulation results without the large pores ($Φ=0$) are similar to those of a formerly studied model of corrosion and passivation and are explained by a scaling approach. If $Φ>0$ and $D_{\text r}\ll 1$, significant changes are observed in passive layer growth and corrosion front roughness. For small $Φ$, a slowdown of the growth rate is observed, which is interpreted as a consequence of the confinement of anions in isolated pores for long times. However, the presence of large pores near the corrosion front increases the frequency of reactions at those regions, which leads to an increase in the roughness of that front. This model may be a first step to represent defects in a passive layer which favor pitting corrosion. △ Less

Submitted 4 October, 2017; originally announced October 2017.

Comments: 8 pages, 6 figures

Journal ref: Condens. Matter Phys., 2017, vol. 20, No. 3, 33803

Scaling relations in the diffusive infiltration in fractals

Authors: F. D. A. Aarao Reis

Abstract: In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as F~t^n, with n<1/2, thus providing a macroscopic realization of anomalous diffusion [Filipovitch et al, Water Resour. Res. 52 5167 (2016)]. The results agree with simulations of a diffusion equation with constant pressure at… ▽ More In a recent work on fluid infiltration in a Hele-Shaw cell with the pore-block geometry of Sierpinski carpets (SCs), the area filled by the invading fluid was shown to scale as F~t^n, with n<1/2, thus providing a macroscopic realization of anomalous diffusion [Filipovitch et al, Water Resour. Res. 52 5167 (2016)]. The results agree with simulations of a diffusion equation with constant pressure at one of the borders of those fractals, but the exponent n is very different from the anomalous exponent nu=1/D_W of single particle diffusion in the same fractals (D_W is the random walk dimension). Here we use a scaling approach to show that those exponents are related as n=nu(D_F-D_B), where D_F and D_B are the fractal dimensions of the bulk and of the border from which diffusing particles come, respectively. This relation is supported by accurate numerical estimates in two SCs and in two generalized Menger sponges (MSs), in which we performed simulations of single particle random walks (RWs) with a rigid impermeable border and of a diffusive infiltration model in which that border is permanently filled with diffusing particles. This study includes one MS whose external border is also fractal. The exponent relation is also consistent with the recent simulational and experimental results on fluid infiltration in SCs, and explains the approximate quadratic dependence of n on D_F in these fractals. We also show that the mean-square displacement of single particle RWs has log-periodic oscillations, whose periods are similar for fractals with the same scaling factor in the generator (even with different embedding dimensions), which is consistent with the discrete scale invariance scenario. The roughness of a diffusion front defined in the infiltration problem also shows this type of oscillation, which is enhanced in fractals with narrow channels between large lacunas. △ Less

Submitted 23 May, 2017; originally announced May 2017.

Comments: 17 pages with 11 figures

Journal ref: Phys. Rev. E 94, 052124 (2016)

Double Band Inversion in $ α$-Sn: Appearance of Topological Surface States and the Role of Orbital Composition

Authors: Victor A. Rogalev, Tomáš Rauch, Markus R. Scholz, Felix Reis, Lenart Dudy, Andrzej Fleszar, Marius-Adrian Husanu, Vladimir N. Strocov, Jürgen Henk, Ingrid Mertig, Jörg Schäfer, Ralph Claessen

Abstract: The electronic structure of \graySn(001) thin films strained compressively in-plane was studied both experimentally and theoretically. A new topological surface state (TSS) located entirely within the gapless projected bulk bands is revealed by \textit{ab initio}-based tight-binding calculations as well as directly accessed by soft X-ray angle-resolved photoemission. The topological character of t… ▽ More The electronic structure of \graySn(001) thin films strained compressively in-plane was studied both experimentally and theoretically. A new topological surface state (TSS) located entirely within the gapless projected bulk bands is revealed by \textit{ab initio}-based tight-binding calculations as well as directly accessed by soft X-ray angle-resolved photoemission. The topological character of this state, which is a surface resonance, is confirmed by unravelling the band inversion and by calculating the topological invariants. In agreement with experiment, electronic structure calculations show the maximum density of states in the subsurface region, while the already established TSS near the Fermi level is strongly localized at the surface. Such varied behavior is explained by the differences in orbital composition between the specific TSS and its associated bulk states, respectively. This provides an orbital protection mechanism for topological states against mixing with the background of bulk bands. △ Less

Submitted 16 February, 2017; v1 submitted 12 January, 2017; originally announced January 2017.

Journal ref: Phys. Rev. B 95, 161117 (2017)

Random sequential adsorption of polydisperse mixtures on lattices

Authors: Rogerio Costa Hart, Fabio David Alves Aarão Reis

Abstract: Random sequential adsorption of linear and square particles with excluded volume interaction is studied numerically on planar lattices considering Gaussian distributions of lateral sizes of the incident particles, with several values of the average and of the width-to-average ratio $w$. When the coverage is plotted as function of the logarithm of time $t$, the maximum slope is attained at a time… ▽ More Random sequential adsorption of linear and square particles with excluded volume interaction is studied numerically on planar lattices considering Gaussian distributions of lateral sizes of the incident particles, with several values of the average and of the width-to-average ratio $w$. When the coverage is plotted as function of the logarithm of time $t$, the maximum slope is attained at a time $t_M$ of the same order of the time $τ$ of incidence of one monolayer, which is related to the molecular flux and/or sticking coefficients. For various values of the average $μ$ and $w$, we obtain $1.5τ< t_M < 5τ$ for linear particles and $.3τ< t_M < τ$ for square particles. At $t_M$, the coverages with linear and square particles are near .3 and .2, respectively. Extrapolations show that coverages may vary with $μ$ up to 20% and 2% for linear and square particles, respectively, for $μ\ge 64$, fixed time, and constant $w$. All coverage $θ$ versus $\log t$ plots have approximately the same shape, but other quantities measured at times of order $t_M$ help to distinguish narrow and broad incident distributions. The adsorbed particle size distributions are close to the incident ones up to long times for small $w$, but appreciably change in time for larger $w$, acquiring a monotonically decreasing shape for $w = 1/2$ at times of order $100τ$ . At $t_M$, incident and adsorbed distributions are approximately the same for $w \le 1/8$ and show significant differences for $w \ge 1/2$; this result may be used as a consistency test in applications of the model. The pair correlation function $g (r; t)$ for $w = 1/8$ has a well defined oscillatory structure at $10t_M$, with a minimum at $r\approxμ$ and maximum at $r \approx 1.5μ$, but this structure is not observed for $w \ge 1/4$. △ Less

Submitted 9 August, 2016; originally announced August 2016.

Comments: 15 pages, 14 figures

Bismuthene on a SiC Substrate: A Candidate for a New High-Temperature Quantum Spin Hall Paradigm

Authors: F. Reis, G. Li, L. Dudy, M. Bauernfeind, S. Glass, W. Hanke, R. Thomale, J. Schäfer, R. Claessen

Abstract: Quantum spin Hall (QSH) materials promise revolutionary device applications based on dissipationless propagation of spin currents. They are two-dimensional (2D) representatives of the family of topological insulators, which exhibit conduction channels at their edges inherently protected against scattering. Initially predicted for graphene, and eventually realized in HgTe quantum wells, in the QSH… ▽ More Quantum spin Hall (QSH) materials promise revolutionary device applications based on dissipationless propagation of spin currents. They are two-dimensional (2D) representatives of the family of topological insulators, which exhibit conduction channels at their edges inherently protected against scattering. Initially predicted for graphene, and eventually realized in HgTe quantum wells, in the QSH systems realized so far, the decisive bottleneck preventing applications is the small bulk energy gap of less than 30 meV, requiring cryogenic operation temperatures in order to suppress detrimental bulk contributions to the edge conductance. Room-temperature functionalities, however, require much larger gaps. Here we show how this can be achieved by making use of a new QSH paradigm based on substrate-supported atomic monolayers of a high-Z element. Experimentally, the material is synthesized as honeycomb lattice of bismuth atoms, forming "bismuthene", on top of the wide-gap substrate SiC(0001). Consistent with the theoretical expectations, the spectroscopic signatures in experiment display a huge gap of ~0.8 eV in bismuthene, as well as conductive edge states. The analysis of the layer-substrate orbitals arrives at a QSH phase, whose topological gap - as a hallmark mechanism - is driven directly by the atomic spin-orbit coupling (SOC). Our results demonstrate how strained artificial lattices of heavy atoms, in contact with an insulating substrate, can be utilized to evoke a novel topological wide-gap scenario, where the chemical potential is located well within the global system gap, ensuring pure edge state conductance. We anticipate future experiments on topological signatures, such as transport measurements that probe the QSH effect via quantized universal conductance, notably at room temperature. △ Less

Submitted 2 August, 2016; originally announced August 2016.

Comments: 4 figures

Journal ref: Science 357, 287-290 (2017)

Transition from compact to porous films in deposition with temperature activated diffusion

Authors: Dung di Caprio, F. D. A. Aarao Reis

Abstract: We study a thin film growth model with temperature activated diffusion of adsorbed particles, allowing for the formation of overhangs and pores, but without detachment of adatoms or clusters from the deposit. Simulations in one-dimensional substrates are performed for several values of the diffusion-to-deposition ratio R of adatoms with a single bond and of the detachment probability epsilon per a… ▽ More We study a thin film growth model with temperature activated diffusion of adsorbed particles, allowing for the formation of overhangs and pores, but without detachment of adatoms or clusters from the deposit. Simulations in one-dimensional substrates are performed for several values of the diffusion-to-deposition ratio R of adatoms with a single bond and of the detachment probability epsilon per additional nearest neighbor (NN), respectively with activation energies are Es and Eb. If R and epsilon independently vary, regimes of low and high porosity are separated at 0.075 < epsilon_c < 0.09, with vanishingly small porosity below that point and finite porosity for larger epsilon. Alternatively, for fixed values of Es and Eb and varying temperature, the porosity has a minimum at Tc, and a nontrivial regime in which it increases with temperature is observe above that point. This is related to the large mobility of adatoms, resembling features of equilibrium surface roughening. In this high-temperature region, the deposit has the structure of a critical percolation cluster due to the non-desorption condition. The pores are regions enclosed by blobs of the corresponding percolating backbone, thus the distribution of pore size s is expected to scale as s^{-tau} with tau ~ 1.45, in reasonable agreement with numerical estimates. Roughening of the outer interface of the deposits suggests Villain-Lai-Das Sarma scaling below the transition. Above the transition, the roughness exponent alpha ~ 0.35 is consistent with the percolation backbone structure via the relation alpha = 2-d_B, where d_B is the backbone fractal dimension. △ Less

Submitted 30 November, 2015; originally announced December 2015.

Comments: 15 pages, 10 figures

Journal ref: Phys. Rev. E 92, 012402 (2015)

Scaling of local roughness distributions

Authors: Fabio D. A. Aarao Reis

Abstract: Local roughness distributions (LRDs) are studied in the growth regimes of lattice models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 and 2+1 dimensions and in a model of the Villain-Lai-Das Sarma (VLDS) growth class in 2+1 dimensions. The squared local roughness w_2 is defined as the variance of the height inside a box of lateral size r and the LRD P_r(w_2) is sampled as this box glides along a… ▽ More Local roughness distributions (LRDs) are studied in the growth regimes of lattice models in the Kardar-Parisi-Zhang (KPZ) class in 1+1 and 2+1 dimensions and in a model of the Villain-Lai-Das Sarma (VLDS) growth class in 2+1 dimensions. The squared local roughness w_2 is defined as the variance of the height inside a box of lateral size r and the LRD P_r(w_2) is sampled as this box glides along a surface with size L >> r. The variation coefficient C and the skewness S of the distributions are functions of the scaled box size r / xi, where xi(t) is a correlation length. For r <~ 0.3 xi, plateaus of C and S are observed, but with a small time dependence. For a quantitative characterization of the universal LRD, extrapolation of these values with power-law corrections in time are performed. The reliability of this procedure is confirmed in 1+1 dimensions by comparison of results of the restricted solid-on-solid model and theoretically predicted values of Edwards-Wilkinson interfaces. For r >> xi, C and S vanish because the LRD converges to a Dirac delta function. This confirms the inadequacy of extrapolations of amplitude ratios to r -> infinity, as proposed in recent works. On the other hand, it highlights the advantage of scaling LRDs by the average instead of scaling by the variance due to the usually higher accuracy of C compared to S. The scaled LRD of the VLDS model is very close to the KPZ one due to the small difference between their variation coefficients and the plateaus of C and S are very narrow due to the slow time increase of xi. These results suggest that experimental LRDs obtained in short growth times and with limited resolution may be inconclusive to determine their universality classes if data accuracy is low and/or data extrapolation to the long time limit is not feasible. △ Less

Submitted 6 November, 2015; originally announced November 2015.

Comments: 10 pages in double-column format, 13 figures included, accepted in JSTAT

Substrate effects and diffusion dominated roughening in Cu2O electrodeposition

Authors: I. S. Brandt, V. C. Zoldan, V. Stenger, C. C. Pla Cid, A. A. Pasa, T. J. Oliveira, F. D. A. Aarao Reis

Abstract: Cuprous oxide (Cu2O) films from 25 nm to 1500 nm were electrodeposited on n-Si(100) and Ni/n-Si(100) substrates from aqueous solution at room temperature. X-ray diffraction and transmission electron microscopy imaging show that the Cu2O structure and morphology is strongly affected by the substrate choice, with V shape and U shape columnar growth on n-Si(100) and Ni/n-Si(100), respectively. Atomic… ▽ More Cuprous oxide (Cu2O) films from 25 nm to 1500 nm were electrodeposited on n-Si(100) and Ni/n-Si(100) substrates from aqueous solution at room temperature. X-ray diffraction and transmission electron microscopy imaging show that the Cu2O structure and morphology is strongly affected by the substrate choice, with V shape and U shape columnar growth on n-Si(100) and Ni/n-Si(100), respectively. Atomic force microscopy reveals the presence of rounded grains at the surface in both cases. Anomalous and normal roughening are observed in films grown on n-Si and Ni, respectively, but estimates of scaling exponents are not conclusive. On the other hand, the distributions of local heights, roughness, and extremal heights show good agreement with those of the fourth order linear stochastic equation of Mullins and Herring (MH). Thus, surface dynamics in both systems is dominated by diffusion of adsorbed molecules, with no large scale effect of possible inhomogeneities in mass flux from the solution or in reaction and adsorption rates. In growth on n-Si substrates, the noise amplitude of the MH equation increases in time as t^{0.8}, while the coefficient of the curvature-related term is time-independent. Step edge energy barriers restrict the mass flux across grain boundaries, thus a broad size distribution of initial grains leads to coarsening of the larger ones. This explains their V shape in the thickest films and establishes a connection with the anomalous roughening. These effects are reduced in films grown on Ni/n-Si, which initially have much larger grains with narrower size distributions and, consequently, smaller fluctuations in coarse grained growth rates. △ Less

Submitted 15 September, 2015; originally announced September 2015.

Comments: 11 pages, 9 figures

Journal ref: J. Appl. Phys. 118, 145303 (2015)

Crossover from anomalous to normal diffusion in porous media

Authors: F. D. A. Aarao Reis, Dung di Caprio

Abstract: Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores, in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover… ▽ More Random walks (RW) of particles adsorbed in the internal walls of porous deposits produced by ballistic-type growth models are studied. The particles start at the external surface of the deposits and enter their pores, in order to simulate an external flux of a species towards a porous solid. For short times, the walker concentration decays as a stretched exponential of the depth z, but a crossover to long time normal diffusion is observed in most samples. The anomalous concentration profile remains at long times in very porous solids if the walker steps are restricted to nearest neighbors and is accompanied with subdiffusion features. These findings are correlated with a decay of the explored area with z. The study of RW of tracer particles left at the internal part of the solid rules out an interpretation by diffusion equations with position-dependent coefficients. A model of RW in a tube of decreasing cross section explains those results by showing long crossovers from an effective subdiffusion regime to an asymptotic normal diffusion. The crossover position and density are analytically calculated for a tube with area decreasing exponentially with z and show good agreement with numerical data. The anomalous decay of the concentration profile is interpreted as a templating effect of the tube shape on the total number of diffusing particles at each depth, while the volumetric concentration in the actually explored porous region may not have significant decay. These results may explain the anomalous diffusion of metal atoms in porous deposits observed in recent works. They also confirm the difficulty in interpreting experimental or computational data on anomalous transport reported in recent works, particularly if only the concentration profiles are measured. △ Less

Submitted 16 June, 2015; originally announced June 2015.

Comments: 11 pages, 10 figures included

Journal ref: Phys. Rev. E 89, 062126 (2014)

Kinetic roughening and porosity scaling in film growth with subsurface lateral aggregation

Authors: Fabio D. A. Aarao Reis

Abstract: We study surface and bulk properties of porous films produced by a model in which particles incide perpendicularly to a substrate, interact with deposited neighbors in its trajectory, and aggregate laterally with probability of order $a$ at each position. The model generalizes ballistic-like models by allowing attachment to particles below the outer surface. For small values of $a$, a crossover fr… ▽ More We study surface and bulk properties of porous films produced by a model in which particles incide perpendicularly to a substrate, interact with deposited neighbors in its trajectory, and aggregate laterally with probability of order $a$ at each position. The model generalizes ballistic-like models by allowing attachment to particles below the outer surface. For small values of $a$, a crossover from uncorrelated deposition (UD) to correlated growth is observed. Simulations are performed in 1+1 and 2+1 dimensions. Extrapolation of effective exponents and comparison of roughness distributions confirm Kardar-Parisi-Zhang roughening of the outer surface for $a>0$. A scaling approach for small $a$ predicts crossover times as $a^{-2/3}$ and local height fluctuations as $a^{-1/3}$ at the crossover, independently of substrate dimension. These relations are different from all previously studied models with crossovers from UD to correlated growth due to subsurface aggregation, which reduces scaling exponents. The same approach predicts the porosity and average pore height scaling as $a^{1/3}$ and $a^{-1/3}$, respectively, in good agreement with simulation results in 1+1 and 2+1 dimensions. These results may be useful to modeling samples with desired porosity and long pores. △ Less

Submitted 8 June, 2015; originally announced June 2015.

Comments: 9 pages, 10 figures included, to appear in Phys. Rev. E

Dynamic scaling and temperature effects in thin film roughening

Authors: T. A. de Assis, F. D. A. Aarão Reis

Abstract: The dynamic scaling of mesoscopically thick films (up to $10^{4}$ atomic layers) grown with the Clarke-Vvedensky model is investigated numerically for broad ranges of values of the diffusion-to-deposition ratio $R$ and lateral neighbor detachment probability $ε$, but with no barrier at step edges. The global roughness scales with the film thickness $t$ as… ▽ More The dynamic scaling of mesoscopically thick films (up to $10^{4}$ atomic layers) grown with the Clarke-Vvedensky model is investigated numerically for broad ranges of values of the diffusion-to-deposition ratio $R$ and lateral neighbor detachment probability $ε$, but with no barrier at step edges. The global roughness scales with the film thickness $t$ as $W \sim t^β/\left[R^{3/2}\left(ε+ a\right)\right]$, where $β\approx 0.2$ is the growth exponent consistent with Villain-Lai-Das Sarma (VLDS) scaling and $a=0.025$. This general dependence on $R$ and $ε$ is inferred from renormalization studies and shows a remarkable effect of the former but a small effect of the latter, for $ε\leq 0.1$. For $R\geq {10}^4$, very smooth surfaces are always produced. The local roughness shows apparent anomalous scaling for very low temperatures ($R\leq {10}^2$), which is a consequence of large scaling corrections to asymptotic normal scaling. The scaling variable $R^{3/2}\left( ε+ a\right)$ also represents the temperature effects in the scaling of the correlation length and appears in the dynamic scaling relation of the local roughness, which gives dynamic exponent $z\approx 3.3$ also consistent with the VLDS class. △ Less

Submitted 16 April, 2015; originally announced April 2015.

Signatures of Dirac fermion-mediated magnetic order

Authors: Paolo Sessi, Felix Reis, Thomas Bathon, Konstantin A. Kokh, Oleg. E. Tereshchenko, Matthias Bode

Abstract: The spin-momentum locking of topological states offers an ideal platform to explore novel magneto-electric effects. These intimately depend on the ability to manipulate the spin texture in a controlled way. Here, we combine scanning tunneling microscopy with single atoms deposition to map the evolution of topological states under the influence of different magnetic perturbations. We obtain signatu… ▽ More The spin-momentum locking of topological states offers an ideal platform to explore novel magneto-electric effects. These intimately depend on the ability to manipulate the spin texture in a controlled way. Here, we combine scanning tunneling microscopy with single atoms deposition to map the evolution of topological states under the influence of different magnetic perturbations. We obtain signatures of Dirac fermion-mediated magnetic order for extremely dilute adatoms concentrations. This striking observation is found to critically depend on the single adatoms magnetic anisotropy and the position of the Fermi level. Our findings open new perspectives in spin engineering topological states at the atomic scale and pave the way to explore novel spin-related topological phenomena with promising potential for applications. △ Less

Submitted 30 October, 2014; originally announced October 2014.

Journal ref: Nature Communications 5, 5349 (2014)

Relaxation after a change in the interface growth dynamics

Authors: T. A. de Assis, F. D. A. Aarão Reis

Abstract: The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments and simulation results are combined to predict the relaxation of the difference in the roughness of the perturbed and the unperturbed interfaces,… ▽ More The global effects of sudden changes in the interface growth dynamics are studied using models of the Edwards-Wilkinson (EW) and Kardar-Parisi-Zhang (KPZ) classes during their growth regimes in dimensions $d=1$ and $d=2$. Scaling arguments and simulation results are combined to predict the relaxation of the difference in the roughness of the perturbed and the unperturbed interfaces, $ΔW^2 \sim s^c t^{-γ}$, where $s$ is the time of the change and $t>s$ is the observation time after that event. The previous analytical solution for the EW-EW changes is reviewed and numerically discussed in the context of lattice models, with possible decays with $γ=3/2$ and $γ=1/2$. Assuming the dominant contribution to $ΔW^2$ to be predicted from a time shift in the final growth dynamics, the scaling of KPZ-KPZ changes with $γ= 1-2β$ and $c=2β$ is predicted, where $β$ is the growth exponent. Good agreement with simulation results in $d=1$ and $d=2$ is observed. A relation with the relaxation of a local autoresponse function in $d=1$ cannot be discarded, but very different exponents are shown in $d=2$. We also consider changes between different dynamics, with the KPZ-EW as a special case in which a faster growth, with dynamical exponent $z_i$, changes to a slower one, with exponent $z$. A scaling approach predicts a crossover time $t_c\sim s^{z/z_i}\gg s$ and $ΔW^2 \sim s^c F\left( t/t_c\right)$, with the decay exponent $γ=1/2$ of the EW class. This rules out the simplified time shift hypothesis in $d=2$ dimensions. These results help to understand the remarkable differences in EW smoothing of correlated and uncorrelated surfaces, and the approach may be extended to sudden changes between other growth dynamics. △ Less

Submitted 3 June, 2014; v1 submitted 23 January, 2014; originally announced January 2014.

Comments: Accepted - Physical Review E

Journal ref: Phys. Rev. E 89, 062405 2014

Simulating the initial growth of a deposit from colloidal suspensions

Authors: T. J. Oliveira, F. D. A. Aarao Reis

Abstract: We study the short time properties of a two-dimensional film growth model in which incident particles execute advective-diffusive motion with a vertical step followed by $D$ horizontal steps. The model represents some features of the deposition of anisotropic colloidal particles of the experiment in Phys. Rev. Lett. {\bf 110}, 035501 (2013), in which wandering particles are attracted to particle-r… ▽ More We study the short time properties of a two-dimensional film growth model in which incident particles execute advective-diffusive motion with a vertical step followed by $D$ horizontal steps. The model represents some features of the deposition of anisotropic colloidal particles of the experiment in Phys. Rev. Lett. {\bf 110}, 035501 (2013), in which wandering particles are attracted to particle-rich regions in the deposit. Height profiles changing from rough to columnar structure are observed as $D$ increases from $0$ (ballistic deposition) to $8$, with striking similarity to the experimental ones. The effective growth exponents matches the experimental estimates and the scaling of those exponents on $D$ show a remarkable effect of the range of the particle-deposit interaction. The nearly ellipsoidal shape of colloidal particles is represented for the calculation of roughness exponents in conditions that parallel the experimental ones, giving a range of estimates that also include the experimental values. The effective dynamic exponents calculated from the autocorrelation function are shown to be suitable to decide between a true dynamic scaling or transient behavior, particularly because the latter leads to deviations in an exponent relation. These results are consistent with arguments on short time unstable (columnar) growth of Phys. Rev. Lett {\bf 111}, 209601 (2013), indicating that critical quenched KPZ dynamics does not explain that colloidal particle deposition problem. △ Less

Submitted 8 July, 2014; v1 submitted 3 January, 2014; originally announced January 2014.

Comments: 14 pages, 6 figures

Journal ref: J. Stat. Mech. (2014) P09006

Universal fluctuations in the growth of semiconductor thin films

Authors: R. A. L. Almeida, S. O. Ferreira, T. J. Oliveira, F. D. A. Aarao Reis

Abstract: Scaling of surface fluctuations of polycrystalline CdTe/Si(100) films grown by hot wall epitaxy are studied. The growth exponent of surface roughness and the dynamic exponent of the auto-correlation function in the mound growth regime agree with the values of the Kardar-Parisi-Zhang (KPZ) class. The scaled distributions of heights, local roughness, and extremal heights show remarkable collapse wit… ▽ More Scaling of surface fluctuations of polycrystalline CdTe/Si(100) films grown by hot wall epitaxy are studied. The growth exponent of surface roughness and the dynamic exponent of the auto-correlation function in the mound growth regime agree with the values of the Kardar-Parisi-Zhang (KPZ) class. The scaled distributions of heights, local roughness, and extremal heights show remarkable collapse with those of the KPZ class, giving the first experimental observation of KPZ distributions in $2+1$ dimensions. Deviations from KPZ values in the long-time estimates of dynamic and roughness exponents are explained by spurious effects of multi-peaked coalescing mounds and by effects of grain shapes. Thus, this scheme for investigating universality classes of growing films advances over the simple comparison of scaling exponents. △ Less

Submitted 5 December, 2013; originally announced December 2013.

Comments: 5 pages, 3 figures

Journal ref: Phys. Rev. B 89, 045309 (2014)

Thin film deposition with time varying temperature

Authors: T. A. de Assis, F. D. A. A. Reis

Abstract: We study the effects of time-dependent substrate/film temperature in the deposition of a mesoscopically thick film using a statistical model that accounts for diffusion of adatoms without lateral neighbors whose coefficients depend on an activation energy and temperature. Dynamic scaling with fixed temperature is extended to predict conditions in which the temperature variation significantly affec… ▽ More We study the effects of time-dependent substrate/film temperature in the deposition of a mesoscopically thick film using a statistical model that accounts for diffusion of adatoms without lateral neighbors whose coefficients depend on an activation energy and temperature. Dynamic scaling with fixed temperature is extended to predict conditions in which the temperature variation significantly affects surface roughness scaling. It agrees with computer simulation results for deposition of up to ${10}^4$ atomic layers and maximal temperature changes of $30 K$, near or below the room temperature. If the temperature decreases during the growth, the global roughness may have a rapid growth, with effective exponents larger than 1/2 due to the time-decreasing adatom mobility. The local roughness in small box size shows typical evidence of anomalous scaling, with anomaly exponents depending on the particular form of temperature decrease. If the temperature increases during the growth, a non-monotonic evolution of the global roughness may be observed, which is explained by the competition of kinetic roughening and the smoothing effect of increasing diffusion lengths. The extension of the theoretical approach to film deposition with other activation energy barriers shows that similar conditions on temperature variation may lead to the same morphological features. Equivalent results may also be observed by controlling the deposition flux. △ Less

Submitted 14 September, 2013; v1 submitted 20 March, 2013; originally announced March 2013.

Comments: 18 pages, 8 figures

MSC Class: 82

Journal ref: J. Stat. Mech. (2013) P10008

Scaling in reversible submonolayer deposition

Authors: T. J. Oliveira, F. D. A. Aarao Reis

Abstract: The scaling of island and monomer density, capture zone distributions (CZDs), and island size distributions (ISDs) in reversible submonolayer growth was studied using the Clarke-Vvedensky model. An approach based on rate-equation results for irreversible aggregation (IA) models is extended to predict several scaling regimes in square and triangular lattices, in agreement with simulation results. C… ▽ More The scaling of island and monomer density, capture zone distributions (CZDs), and island size distributions (ISDs) in reversible submonolayer growth was studied using the Clarke-Vvedensky model. An approach based on rate-equation results for irreversible aggregation (IA) models is extended to predict several scaling regimes in square and triangular lattices, in agreement with simulation results. Consistently with previous works, a regime I with fractal islands is observed at low temperatures, corresponding to IA with critical island size i=1, and a crossover to a second regime appears as the temperature is increased to εR^{2/3} ~ 1, where εis the single bond detachment probability and R is the diffusion-to-deposition ratio. In the square (triangular) lattice, a regime with scaling similar to IA with i=3 (i=2) is observed after that crossover. In the triangular lattice, a subsequent crossover to an IA regime with i=3 is observed, which is explained by the recurrence properties of random walks in two dimensional lattices, which is beyond the mean-field approaches. At high temperatures, a crossover to a fully reversible regime is observed, characterized by a large density of small islands, a small density of very large islands, and total island and monomer densities increasing with temperature, in contrast to IA models. CZDs and ISDs with Gaussian right tails appear in all regimes for R ~ 10^7 or larger, including the fully reversible regime, where the CZDs are bimodal. This shows that the Pimpinelli-Einstein (PE) approach for IA explains the main mechanisms for the large islands to compete for free adatom aggregation in the reversible model, and may be the reason for its successful application to a variety of materials and growth conditions. △ Less

Submitted 10 June, 2013; v1 submitted 5 March, 2013; originally announced March 2013.

Comments: 10 pages, 7 figures

Journal ref: Phys. Rev. B 87, 235430 (2013)

Langevin equations for competitive growth models

Authors: F. A. Silveira, F. D. A. Aarao Reis

Abstract: Langevin equations for several competitive growth models in one dimension are derived. For models with crossover from random deposition (RD) to some correlated deposition (CD) dynamics, with small probability p of CD, the surface tension νand the nonlinear coefficient λof the associated equations have linear dependence on p due solely to this random choice. However, they also depend on the regular… ▽ More Langevin equations for several competitive growth models in one dimension are derived. For models with crossover from random deposition (RD) to some correlated deposition (CD) dynamics, with small probability p of CD, the surface tension νand the nonlinear coefficient λof the associated equations have linear dependence on p due solely to this random choice. However, they also depend on the regularized step functions present in the analytical representations of the CD, whose expansion coefficients scale with p according to the divergence of local height differences when p->0. The superposition of those scaling factors gives ν~ p^2 for random deposition with surface relaxation (RDSR) as the CD, and ν~ p, λ~ p^{3/2} for ballistic deposition (BD) as the CD, in agreement with simulation and other scaling approaches. For bidisperse ballistic deposition (BBD), the same scaling of RD-BD model is found. The Langevin equation for the model with competing RDSR and BD, with probability p for the latter, is also constructed. It shows linear p-dependence of λ, while the quadratic dependence observed in previous simulations is explained by an additional crossover before the asymptotic regime. The results highlight the relevance of scaling of the coefficients of step function expansions in systems with steep surfaces, which is responsible for noninteger exponents in some p-dependent stochastic equations, and the importance of the physical correspondence of aggregation rules and equation coefficients. △ Less

Submitted 3 February, 2013; originally announced February 2013.

Comments: 8 pages with 1 figure included

Journal ref: Phys. Rev. E 85, 011601 (2012)

Anomalous roughening in competitive growth models with time-decreasing rates of correlated dynamics

Authors: Fabio D. A. Aarao Reis

Abstract: Lattice growth models where uncorrelated random deposition competes with some aggregation dynamics that generates correlations are studied with rates of the correlated component decreasing as a power law. These models have anomalous roughening, with anomalous exponents related to the normal exponents of the correlated dynamics, to an exponent characterizing the aggregation mechanism and to that po… ▽ More Lattice growth models where uncorrelated random deposition competes with some aggregation dynamics that generates correlations are studied with rates of the correlated component decreasing as a power law. These models have anomalous roughening, with anomalous exponents related to the normal exponents of the correlated dynamics, to an exponent characterizing the aggregation mechanism and to that power law exponent. This is shown by a scaling approach extending the Family-Vicsek relation previously derived for the models with time-independent rates, thus providing a connection of normal and anomalous growth models. Simulation results for several models support those conclusions. Remarkable anomalous effects are observed even for slowly decreasing rates of the correlated component, which may correspond to feasible temperature changes in systems with activated dynamics. The scaling exponents of the correlated component can be obtained only from the estimates of three anomalous exponents, without knowledge of the aggregation mechanism, and a possible application is discussed. For some models, the corresponding Edwards-Wilkinson and Kardar-Parisi-Zhang equations are also discussed. △ Less

Submitted 3 February, 2013; originally announced February 2013.

Comments: 8 pages with 6 figures included

Journal ref: Phys. Rev. E 84, 031604 (2011)

Crossover in the scaling of island size and capture zone distributions

Authors: T. J. Oliveira, F. D. A. Aarao Reis

Abstract: Simulations of irreversible growth of extended (fractal and square) islands with critical island sizes i=1 and 2 are performed in broad ranges of coverage θand diffusion-to-deposition ratios R in order to investigate scaling of island size and capture zone area distributions (ISD, CZD). Large θand small R lead to a crossover from the CZD predicted by the theory of Pimpinelli and Einstein (PE), wit… ▽ More Simulations of irreversible growth of extended (fractal and square) islands with critical island sizes i=1 and 2 are performed in broad ranges of coverage θand diffusion-to-deposition ratios R in order to investigate scaling of island size and capture zone area distributions (ISD, CZD). Large θand small R lead to a crossover from the CZD predicted by the theory of Pimpinelli and Einstein (PE), with Gaussian right tail, to CZD with simple exponential decays. The corresponding ISD also cross over from Gaussian or faster decays to simple exponential ones. For fractal islands, these features are explained by changes in the island growth kinetics, from a competition for capture of diffusing adatoms (PE scaling) to aggregation of adatoms with effectively irrelevant diffusion, which is characteristic of random sequential adsorption (RSA) without surface diffusion. This interpretation is confirmed by studying the crossover with similar CZ areas (of order 100 sites) in a model with freezing of diffusing adatoms that corresponds to i=0. For square islands, deviations from PE predictions appear for coverages near θ=0.2 and are mainly related to island coalescence. Our results show that the range of applicability of the PE theory is narrow, thus observing the predicted Gaussian tail of CZD may be difficult in real systems. △ Less

Submitted 7 August, 2012; originally announced August 2012.

Comments: 9 pages, 7 figures

Journal ref: Phys. Rev. B 86, 115402 (2012)

Induced Optical Losses in Optoelectronic Devices due to Focused Ion Beam Damages

Authors: Felipe Vallini, Luís Alberto Mijan Barea, Elohim Fonseca dos Reis, Antônio Augusto von Zuben, Newton Cesário Frateschi

Abstract: A study of damages caused by gallium focused ion beam (FIB) into III-V compounds is presented. Potential damages caused by local heating, ion implantation, and selective sputtering are presented. Preliminary analysis shows that local heating is negligible. Gallium implantation is shown to occur over areas tens of nanometers thick. Gallium accumulation as well as selective sputtering during III-V c… ▽ More A study of damages caused by gallium focused ion beam (FIB) into III-V compounds is presented. Potential damages caused by local heating, ion implantation, and selective sputtering are presented. Preliminary analysis shows that local heating is negligible. Gallium implantation is shown to occur over areas tens of nanometers thick. Gallium accumulation as well as selective sputtering during III-V compounds milling is expected. Particularly, for GaAs, this effect leads to gallium segregation and formation of metallic clusters. Microdisk resonators were fabricated using FIB milling with different emission currents to analyze these effects on a device. It is shown that for higher emission current, thus higher implantation doses, the cavity quality factor rapidly decreases due to optical scattering losses induced by implanted gallium atoms. △ Less

Submitted 10 July, 2012; originally announced July 2012.

Scaling of island size and capture zone distributions in submonolayer growth

Authors: T. J. Oliveira, F. D. A. Aarao Reis

Abstract: Island size and capture zone distributions (ISDs, CZDs) are studied numerically in submonolayer growth with various critical island sizes and shapes. CZDs scaled by the variance show excellent agreement with the Wigner surmise, confirming the Pimpinelli-Einstein approach for large CZs / large island dynamics. The ISD decay as exp(-s^x), with x=4, x approx 2.4 and 2 for point, fractal, and square i… ▽ More Island size and capture zone distributions (ISDs, CZDs) are studied numerically in submonolayer growth with various critical island sizes and shapes. CZDs scaled by the variance show excellent agreement with the Wigner surmise, confirming the Pimpinelli-Einstein approach for large CZs / large island dynamics. The ISD decay as exp(-s^x), with x=4, x approx 2.4 and 2 for point, fractal, and square islands, respectively. A scaling approach explains the values of x from the Gaussian decay of CZD and the efficiency of islands to capture diffusing adatoms. △ Less

Submitted 31 May, 2011; originally announced May 2011.

Comments: 12 pages, 3 figures

Journal ref: Phys. Rev. B 83, 201405(R) (2011)

Roughness exponents and grain shapes

Authors: T. J. Oliveira, F. D. A. Aarao Reis

Abstract: In surfaces with grainy features, the local roughness $w$ shows a crossover at a characteristic length $r_c$, with roughness exponent changing from $α_1\approx 1$ to a smaller $α_2$. The grain shape, the choice of $w$ or height-height correlation function (HHCF) $C$, and the procedure to calculate root mean-square averages are shown to have remarkable effects on $α_1$. With grains of pyramidal sha… ▽ More In surfaces with grainy features, the local roughness $w$ shows a crossover at a characteristic length $r_c$, with roughness exponent changing from $α_1\approx 1$ to a smaller $α_2$. The grain shape, the choice of $w$ or height-height correlation function (HHCF) $C$, and the procedure to calculate root mean-square averages are shown to have remarkable effects on $α_1$. With grains of pyramidal shape, $α_1$ can be as low as 0.71, which is much lower than the previous prediction 0.85 for rounded grains. The same crossover is observed in the HHCF, but with initial exponent $χ_1\approx 0.5$ for flat grains, while for some conical grains it may increase to $χ_1\approx 0.7$. The universality class of the growth process determines the exponents $α_2=χ_2$ after the crossover, but has no effect on the initial exponents $α_1$ and $χ_1$, supporting the geometric interpretation of their values. For all grain shapes and different definitions of surface roughness or HHCF, we still observe that the crossover length $r_c$ is an accurate estimate of the grain size. The exponents obtained in several recent experimental works on different materials are explained by those models, with some surface images qualitatively similar to our model films. △ Less

Submitted 16 March, 2011; originally announced March 2011.

Comments: 7 pages, 6 figures and 2 tables

Journal ref: Phys. Rev. E 83, 041608 (2011)

Phase transitions and crossovers in reaction-diffusion models with catalyst deactivation

Authors: T. G. Mattos, Fabio D. A. Aarao Reis

Abstract: The activity of catalytic materials is reduced during operation by several mechanisms, one of them being poisoning of catalytic sites by chemisorbed impurities or products. Here we study the effects of poisoning in two reaction-diffusion models in one-dimensional lattices with randomly distributed catalytic sites. Unimolecular and bimolecular single-species reactions are considered, without reac… ▽ More The activity of catalytic materials is reduced during operation by several mechanisms, one of them being poisoning of catalytic sites by chemisorbed impurities or products. Here we study the effects of poisoning in two reaction-diffusion models in one-dimensional lattices with randomly distributed catalytic sites. Unimolecular and bimolecular single-species reactions are considered, without reactant input during the operation. The models show transitions between a phase with continuous decay of reactant concentration and a phase with asymptotic non-zero reactant concentration and complete poisoning of the catalyst. The transition boundary depends on the initial reactant and catalyst concentrations and on the poisoning probability. The critical system behaves as in the two-species annihilation reaction, with reactant concentration decaying as t^{-1/4} and the catalytic sites playing the role of the second species. In the unimolecular reaction, a significant crossover to the asymptotic scaling is observed even when one of those parameters is 10% far from criticality. Consequently, an effective power-law decay of concentration may persist up to long times and lead to an apparent change in the reaction kinetics. In the bimolecular single-species reaction, the critical scaling is followed by a two-dimensional rapid decay, thus two crossovers are found. △ Less

Submitted 17 June, 2009; originally announced June 2009.

Comments: 8 pages, 7 figures

Effects of diffusion and particle size in a kinetic model of catalyzed reactions

Authors: T. G. Mattos, Fabio D. A. Aarao Reis

Abstract: We study a model for unimolecular reaction on a supported catalyst including reactant diffusion and desorption, using analytical methods and scaling concepts. For rapid reactions, enhancing surface diffusion or increasing particle size favors the flux of reactants to the catalyst particles, which increases the turnover frequency (TOF). The reactant flux towards the support becomes dominant when… ▽ More We study a model for unimolecular reaction on a supported catalyst including reactant diffusion and desorption, using analytical methods and scaling concepts. For rapid reactions, enhancing surface diffusion or increasing particle size favors the flux of reactants to the catalyst particles, which increases the turnover frequency (TOF). The reactant flux towards the support becomes dominant when the ratio of diffusion lengths in the catalyst and in the support exceeds a critical value. A peak in the TOF is obtained for temperature-dependent rates if desorption energy in the support (Ed) exceeds those of diffusion (ED) and reaction (Er). Significant dependence on particle size is observed when the gaps between those energies are small, with small particles giving higher TOF. Slow reactions (Er > Ed) give TOF monotonically increasing with temperature, with higher reactant losses in small particles. The scaling concepts can be extended to interpret experimental data and results of more complex models. △ Less

Submitted 16 June, 2009; originally announced June 2009.

Comments: 9 pages, 7 figures

Journal ref: Journal of Catalysis 263 (2009) 67-74

Modeling self-assembly of diblock copolymer-nanoparticle composites

Authors: Fabio D. A. Aarao Reis

Abstract: A cell dynamics method for domain separation of diblock copolymers (DBCPs) interacting with nanoparticles (NPs) whose diffusion coefficients depend on chain configuration is proposed for self-assembly of DBCP/NP composites. Increasing NP concentration slows down domain separation, but matching NP diffusion lengths and lamellar size of DBCPs reduces this effect. The model also explains features o… ▽ More A cell dynamics method for domain separation of diblock copolymers (DBCPs) interacting with nanoparticles (NPs) whose diffusion coefficients depend on chain configuration is proposed for self-assembly of DBCP/NP composites. Increasing NP concentration slows down domain separation, but matching NP diffusion lengths and lamellar size of DBCPs reduces this effect. The model also explains features of different nanocomposites, such as morphological transitions induced by NPs, the coexistence of lamellar and hexagonal patterns in a single sample and peaked NP density profiles across the parallel domains. △ Less

Submitted 1 April, 2009; originally announced April 2009.

Comments: 21 pages, 7 figures included

Journal ref: Macromolecules 41, 8932-8937 (2008)

Unusual features of coarsening with detachment rates decreasing with cluster mass

Authors: F. D. A. Aarao Reis, R. B. Stinchcombe

Abstract: We study conserved one-dimensional models of particle diffusion, attachment and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) ~ m^{-k}, k>0. Heuristic scaling arguments based on random walk properties show that the typical cluster size scales as (t/ln(t))^z, with z=1/(k+2). The initial symmetric flux of particles between neighboring cluste… ▽ More We study conserved one-dimensional models of particle diffusion, attachment and detachment from clusters, where the detachment rates decrease with increasing cluster size as gamma(m) ~ m^{-k}, k>0. Heuristic scaling arguments based on random walk properties show that the typical cluster size scales as (t/ln(t))^z, with z=1/(k+2). The initial symmetric flux of particles between neighboring clusters is followed by an effectively assymmetric flux due to the unbalanced detachement rates, which leads to the above logarithmic correction. Small clusters have densities of order t^{-mz(1)}, with z(1) = k/(k+2). Thus, for k<1, the small clusters (mass of order unity) are statistically dominant and the average cluster size does not scale as the size of typically large clusters does. We also solve the Master equation of the model under an independent interval approximation, which yields cluster distributions and exponent relations and gives the correct dominant coarsening exponent after accounting for the effects of correlations. The coarsening of large clusters is described by the distribution P_t(m) ~ 1/t^y f(m/t^z), with y=2z. All results are confirmed by simulation, which also illustrates the unusual features of cluster size distributions, with a power law decay for small masses and a negatively skewed peak in the scaling region. The detachment rates considered here can apply in the presence of strong attractive interactions, and recent applications suggest that even more rapid rate decays are also physically realistic. △ Less

Submitted 17 December, 2008; originally announced December 2008.

Comments: 12 pages, with 9 figures included

Journal ref: Phys. Rev. E 77, 041411 (2008)