Showing 1–50 of 91 results for author: Harju, A

Electronic Characterization of a Charge-Transfer Complex Monolayer on Graphene

Authors: Avijit Kumar, Kaustuv Banerjee, Mikko M. Ervasti, Shawulienu Kezilebieke, Marc Dvorak, Patrick Rinke, Ari Harju, Peter Liljeroth

Abstract: Organic charge-transfer complexes (CTCs) formed by strong electron acceptor and strong electron donor molecules are known to exhibit exotic effects such as superconductivity and charge density waves. We present a low-temperature scanning tunneling microscopy and spectroscopy (LT-STM/STS) study of a two-dimensional (2D) monolayer CTC of tetrathiafulvalene (TTF) and fluorinated tetracyanoquinodimeth… ▽ More Organic charge-transfer complexes (CTCs) formed by strong electron acceptor and strong electron donor molecules are known to exhibit exotic effects such as superconductivity and charge density waves. We present a low-temperature scanning tunneling microscopy and spectroscopy (LT-STM/STS) study of a two-dimensional (2D) monolayer CTC of tetrathiafulvalene (TTF) and fluorinated tetracyanoquinodimethane (F4TCNQ), self-assembled on the surface of oxygen-intercalated epitaxial graphene on Ir(111) (G/O/Ir(111)). We confirm the formation of the charge-transfer complex by dI/dV spectroscopy and direct imaging of the singly-occupied molecular orbitals. High-resolution spectroscopy reveals a gap at zero bias, suggesting the formation of a correlated ground state at low temperatures. These results point to the possibility to realize and study correlated ground states in charge-transfer complex monolayers on weakly interacting surfaces. △ Less

Submitted 27 May, 2021; v1 submitted 18 February, 2021; originally announced February 2021.

Comments: Manuscript and Supplementary Information, 36 pages

Journal ref: ACS Nano 15(6), 9945 (2021)

Linear Scaling Quantum Transport Methodologies

Authors: Zheyong Fan, Jose Hugo Garcia, Aron W. Cummings, Jose Eduardo Barrios-Vargas, Michel Panhans, Ari Harju, Frank Ortmann, Stephan Roche

Abstract: In recent years, predictive computational modeling has become a cornerstone for the study of fundamental electronic, optical, and thermal properties in complex forms of condensed matter, including Dirac and topological materials. The simulation of quantum transport in realistic materials calls for the development of linear scaling, or order-$N$, numerical methods, which then become enabling tools… ▽ More In recent years, predictive computational modeling has become a cornerstone for the study of fundamental electronic, optical, and thermal properties in complex forms of condensed matter, including Dirac and topological materials. The simulation of quantum transport in realistic materials calls for the development of linear scaling, or order-$N$, numerical methods, which then become enabling tools for guiding experimental research and for supporting the interpretation of measurements. In this review, we describe and compare different order-$N$ computational methods that have been developed during the past twenty years, and which have been used extensively to explore quantum transport phenomena in disordered media. We place particular focus on the zero-frequency electrical conductivities derived within the Kubo-Greenwood and Kubo-Streda formalisms, and illustrate the capabilities of these methods to tackle the quasi-ballistic, diffusive, and localization regimes of quantum transport in the noninteracting limit. The fundamental issue of computational cost versus accuracy of various proposed numerical schemes is addressed in depth. We then illustrate the usefulness of these methods with various examples of transport in disordered materials, such as polycrystalline and defected graphene models, 3D metals and Dirac semimetals, carbon nanotubes, and organic semiconductors. Finally, we extend the review to the study of spin dynamics and topological transport, for which efficient approaches for calculating charge, spin, and valley Hall conductivities are described. △ Less

Submitted 20 August, 2020; v1 submitted 18 November, 2018; originally announced November 2018.

Comments: 54 pages, 31 figures, Invited Review of Physics Reports

Journal ref: Phys. Rep. 903, 1-69 (2021)

Homogeneous nonequilibrium molecular dynamics method for heat transport and spectral decomposition with many-body potentials

Authors: Zheyong Fan, Haikuan Dong, Ari Harju, Tapio Ala-Nissila

Abstract: The standard equilibrium Green-Kubo and nonequilibrium molecular dynamics (MD) methods for computing thermal transport coefficients in solids typically require relatively long simulation times and large system sizes. To this end, we revisit here the homogeneous nonequilibrium MD method by Evans [Phys. Lett. A \textbf{91}, 457 (1982)] and generalize it to many-body potentials that are required for… ▽ More The standard equilibrium Green-Kubo and nonequilibrium molecular dynamics (MD) methods for computing thermal transport coefficients in solids typically require relatively long simulation times and large system sizes. To this end, we revisit here the homogeneous nonequilibrium MD method by Evans [Phys. Lett. A \textbf{91}, 457 (1982)] and generalize it to many-body potentials that are required for more realistic materials modeling. We also propose a method for obtaining spectral conductivity and phonon mean free path from the simulation data. This spectral decomposition method does not require lattice dynamics calculations and can find important applications in spatially complex structures. We benchmark the method by calculating thermal conductivities of three-dimensional silicon, two-dimensional graphene, and a quasi-one-dimensional carbon nanotube and show that the method is about one to two orders of magnitude more efficient than the Green-Kubo method. We apply the spectral decomposition method to examine the long-standing dispute over thermal conductivity convergence vs divergence in carbon nanotubes. △ Less

Submitted 2 March, 2019; v1 submitted 1 May, 2018; originally announced May 2018.

Comments: 10 pages, 7 figures

Journal ref: Phys. Rev. B 99, 064308 (2019)

Equivalence of the equilibrium and the nonequilibrium molecular dynamics methods for thermal conductivity calculations: From bulk to nanowire silicon

Authors: Haikuan Dong, Zheyong Fan, Libin Shi, Ari Harju, Tapio Ala-Nisilla

Abstract: Molecular dynamics simulations play an important role in studying heat transport in complex materials. The lattice thermal conductivity can be computed either using the Green-Kubo formula in equilibrium MD (EMD) simulations or using Fourier's law in nonequilibrium MD (NEMD) simulations. These two methods have not been systematically compared for materials with different dimensions and inconsistenc… ▽ More Molecular dynamics simulations play an important role in studying heat transport in complex materials. The lattice thermal conductivity can be computed either using the Green-Kubo formula in equilibrium MD (EMD) simulations or using Fourier's law in nonequilibrium MD (NEMD) simulations. These two methods have not been systematically compared for materials with different dimensions and inconsistencies between them have been occasionally reported in the literature. Here we give an in-depth comparison of them in terms of heat transport in three allotropes of Si: three dimensional bulk silicon, two-dimensional silicene, and quasi-one-dimensional silicon nanowire. By multiplying the correlation time in the Green-Kubo formula with an appropriate effective group velocity, we can express the running thermal conductivity in the EMD method as a function of an effective length and directly compare it with the length-dependent thermal conductivity in the NEMD method. We find that the two methods quantitatively agree with each other for all the systems studied, firmly establishing their equivalence in computing thermal conductivity. △ Less

Submitted 1 May, 2018; originally announced May 2018.

Comments: 8 pages, 7 figures

Journal ref: Phys. Rev. B 97, 094305 (2018)

Kapitza thermal resistance across individual grain boundaries in graphene

Authors: Khatereh Azizi, Petri Hirvonen, Zheyong Fan, Ari Harju, Ken R Elder, Tapio Ala-Nissila, S Mehdi Vaez Allaei

Abstract: We study heat transport across individual grain boundaries in suspended monolayer graphene using extensive classical molecular dynamics (MD) simulations. We construct bicrystalline graphene samples containing grain boundaries with symmetric tilt angles using the two-dimensional phase field crystal method and then relax the samples with MD. The corresponding Kapitza resistances are then computed us… ▽ More We study heat transport across individual grain boundaries in suspended monolayer graphene using extensive classical molecular dynamics (MD) simulations. We construct bicrystalline graphene samples containing grain boundaries with symmetric tilt angles using the two-dimensional phase field crystal method and then relax the samples with MD. The corresponding Kapitza resistances are then computed using nonequilibrium MD simulations. We find that the Kapitza resistance depends strongly on the tilt angle and shows a clear correlation with the average density of defects in a given grain boundary, but is not strongly correlated with the grain boundary line tension. We also show that quantum effects are significant in quantitative determination of the Kapitza resistance by applying the mode-by-mode quantum correction to the classical MD data. The corrected data are in good agreement with quantum mechanical Landauer-Bütticker calculations. △ Less

Submitted 27 September, 2017; originally announced September 2017.

Comments: 8 pages, 7 figures

Journal ref: Carbon 125, 384 (2017)

Bimodal grain-size scaling of thermal transport in polycrystalline graphene from large-scale molecular dynamics simulations

Authors: Zheyong Fan, Petri Hirvonen, Luiz Pereira, Mikko Ervasti, Ken Elder, Davide Donadio, Ari Harju, Tapio Ala-Nissila

Abstract: Grain boundaries in graphene are inherent in wafer-scale samples prepared by chemical vapor deposition. They can strongly influence the mechanical properties and electronic and heat transport in graphene. In this work, we employ extensive molecular dynamics simulations to study thermal transport in large suspended polycrystalline graphene samples. Samples of different controlled grain sizes are pr… ▽ More Grain boundaries in graphene are inherent in wafer-scale samples prepared by chemical vapor deposition. They can strongly influence the mechanical properties and electronic and heat transport in graphene. In this work, we employ extensive molecular dynamics simulations to study thermal transport in large suspended polycrystalline graphene samples. Samples of different controlled grain sizes are prepared by a recently developed efficient multiscale approach based on the phase field crystal model. In contrast to previous works, our results show that the scaling of the thermal conductivity with the grain size implies bimodal behaviour with two effective Kapitza lengths. The scaling is dominated by the out-of-plane (flexural) phonons with a Kapitza length that is an order of magnitude larger than that of the in-plane phonons. We also show that in order to get quantitative agreement with the most recent experiments, quantum corrections need to be applied to both the Kapitza conductance of grain boundaries and the thermal conductivity of pristine graphene and the corresponding Kapitza lengths must be renormalized accordingly. △ Less

Submitted 27 September, 2017; originally announced September 2017.

Comments: Accepted to Nano Lett.; Numerical samples and computer codes available

Wave packet dynamics of Bogoliubov quasiparticles: quantum metric effects

Authors: Long Liang, Sebastiano Peotta, Ari Harju, Päivi Törmä

Abstract: We study the dynamics of the Bogoliubov wave packet in superconductors and calculate the supercurrent carried by the wave packet. We discover an anomalous contribution to the supercurrent, related to the quantum metric of the Bloch wave function. This anomalous contribution is most important for flat or quasiflat bands, as exemplified by the attractive Hubbard models on the Creutz ladder and sawto… ▽ More We study the dynamics of the Bogoliubov wave packet in superconductors and calculate the supercurrent carried by the wave packet. We discover an anomalous contribution to the supercurrent, related to the quantum metric of the Bloch wave function. This anomalous contribution is most important for flat or quasiflat bands, as exemplified by the attractive Hubbard models on the Creutz ladder and sawtooth lattice. Our theoretical framework is general and can be used to study a wide variety of phenomena, such as spin transport and exciton transport. △ Less

Submitted 25 July, 2017; v1 submitted 12 May, 2017; originally announced May 2017.

Comments: Updated version, 16 pages, 5 figures, accepted by PRB

Journal ref: Phys. Rev. B 96, 064511 (2017)

Thermal and electronic transport characteristics of highly stretchable graphene kirigami

Authors: Bohayra Mortazavi, Aurélien Lherbier, Zheyong Fan, Ari Harju, Timon Rabczuk, Jean-Christophe Charlier

Abstract: For centuries, cutting and folding the papers with special patterns have been used to build beautiful, flexible and complex three-dimensional structures. Inspired by the old idea of kirigami (paper cutting), and the outstanding properties of graphene, recently graphene kirigami structures were fabricated to enhance the stretchability of graphene. However, the possibility of further tuning the elec… ▽ More For centuries, cutting and folding the papers with special patterns have been used to build beautiful, flexible and complex three-dimensional structures. Inspired by the old idea of kirigami (paper cutting), and the outstanding properties of graphene, recently graphene kirigami structures were fabricated to enhance the stretchability of graphene. However, the possibility of further tuning the electronic and thermal transport along the 2D kirigami structures have remained original to investigate. We therefore performed extensive atomistic simulations to explore the electronic, heat and load transfer along various graphene kirigami structures. The mechanical response and thermal transport were explored using classical molecular dynamics simulations. We then used a real-space Kubo-Greenwood formalism to investigate the charge transport characteristics in graphene kirigami. Our results reveal that graphene kirigami structures present highly anisotropic thermal and electrical transport. Interestingly, we show the possibility of tuning the thermal conductivity of graphene by four orders of magnitude. Moreover, we discuss the engineering of kirigami patterns to further enhance their stretchability by more than 10 times as compared with pristine graphene. Our study not only provides a general understanding concerning the engineering of electronic, thermal and mechanical response of graphene but more importantly can be useful to guide future studies with respect to the synthesis of other 2D material kirigami structures, to reach highly flexible and stretchable nanostructures with finely tunable electronic and thermal properties. △ Less

Submitted 12 April, 2017; originally announced April 2017.

Comments: 29 pages, 9 figures, 1 supplementary figure

Journal ref: Nanoscale, 2017, 9, 16329 - 16341

Amorphized graphene: A stiff material with low thermal conductivity

Authors: B Mortazavi, Z Fan, LFC Pereira, A Harju, T Rabczuk

Abstract: All-carbon heterostructures have been produced recently via focused ion beam patterning of single layer graphene. Amorphized graphene is similar to a graphene sheet in which some hexagons are replaced by a combination of pentagonal, heptagonal and octagonal rings. The present investigation provides a general view regarding phonon and load transfer along amorphous graphene. The developed models for… ▽ More All-carbon heterostructures have been produced recently via focused ion beam patterning of single layer graphene. Amorphized graphene is similar to a graphene sheet in which some hexagons are replaced by a combination of pentagonal, heptagonal and octagonal rings. The present investigation provides a general view regarding phonon and load transfer along amorphous graphene. The developed models for the evaluation of mechanical and thermal conductivity properties yield accurate results for pristine graphene and acquired findings for amorphized graphene films are size independent. Our atomistic results show that amorphous graphene sheets could exhibit a remarkably high elastic modulus of ~500 GPa and tensile strengths of ~50 GPa at room temperature. However, our results show that mechanical properties of amorphous graphene decline at higher temperatures. Furthermore, we show that amorphized graphene present a low thermal conductivity ~15 W/mK which is two orders of magnitude smaller than pristine graphene, and we verify that its thermal conductivity is almost insensitive to temperature since it is dominated by phonon-defect scattering rather than phonon-phonon scattering. Finally, our results show that amorphized graphene structures present a remarkably high elastic modulus and mechanical strength, along with a low thermal conductivity, which is an unusual combination for carbon-based materials. △ Less

Submitted 17 March, 2017; originally announced March 2017.

Journal ref: Carbon 2016, 103, 318-326

Thermal conductivity decomposition in two-dimensional materials: Application to graphene

Authors: Zheyong Fan, Luiz Felipe C. Pereira, Petri Hirvonen, Mikko M. Ervasti, Ken R. Elder, Davide Donadio, Tapio Ala-Nissila, Ari Harju

Abstract: Two-dimensional materials have unusual phonon structures due to the presence of flexural (out-of-plane) modes. Although molecular dynamics simulations have been extensively used to study heat transport in such materials, conventional formalisms treat the phonon dynamics isotropically. Here, we decompose the microscopic heat current in atomistic simulations into in-plane and out-of-plane components… ▽ More Two-dimensional materials have unusual phonon structures due to the presence of flexural (out-of-plane) modes. Although molecular dynamics simulations have been extensively used to study heat transport in such materials, conventional formalisms treat the phonon dynamics isotropically. Here, we decompose the microscopic heat current in atomistic simulations into in-plane and out-of-plane components, corresponding to the in-plane and out-of-plane phonon dynamics, respectively. This decomposition allows for direct computation of the corresponding thermal conductivity components in two-dimensional materials. We apply this decomposition to study heat transport in suspended graphene, using both equilibrium and non-equilibrium molecular dynamics simulations. We show that the flexural component is responsible for about two thirds of the total thermal conductivity in unstrained graphene, and the acoustic flexural component is responsible for the logarithmic divergence of the conductivity when a sufficiently large tensile strain is applied. △ Less

Submitted 25 June, 2017; v1 submitted 21 December, 2016; originally announced December 2016.

Comments: 12 pages, 9 figures

Journal ref: Phys. Rev. B 95, 144309 (2017)

Topological states in engineered atomic lattices

Authors: Robert Drost, Teemu Ojanen, Ari Harju, Peter Liljeroth

Abstract: Topological materials exhibit protected edge modes that have been proposed for applications in for example spintronics and quantum computation. While a number of such systems exist, it would be desirable to be able to test theoretical proposals in an artificial system that allows precise control over the key parameters of the model. The essential physics of several topological systems can be captu… ▽ More Topological materials exhibit protected edge modes that have been proposed for applications in for example spintronics and quantum computation. While a number of such systems exist, it would be desirable to be able to test theoretical proposals in an artificial system that allows precise control over the key parameters of the model. The essential physics of several topological systems can be captured by tight-binding models, which can also be implemented in artificial lattices. Here, we show that this method can be realized in a vacancy lattice in a chlorine monolayer on a Cu(100) surface. We use low-temperature scanning tunneling microscopy (STM) to fabricate such lattices with atomic precision and probe the resulting local density of states (LDOS) with scanning tunneling spectroscopy (STS). We create analogues of two tight-binding models of fundamental importance: The polyacetylene (dimer) chain with topological domain wall states, and the Lieb lattice, featuring a lattice pseudospin 1 system with a flat electron band. These results provide the first steps in realizing designer quantum materials with tailored properties. △ Less

Submitted 11 November, 2016; v1 submitted 3 November, 2016; originally announced November 2016.

Journal ref: Nat. Phys. 13, 668-671 (2017)

Scattering from spin-polarized charged impurities in graphene

Authors: Ville Vierimaa, Zheyong Fan, Ari Harju

Abstract: We study the spin relaxation of charge carriers in graphene in the presence of spin-polarized charged impurities by calculating the time evolution of initially polarized state. The spin relaxation time shows completely different energy behaviour for short-ranged and long-ranged spin scatterers and can be used to identify the dominant source of spin scattering. Our results agree well with recent ex… ▽ More We study the spin relaxation of charge carriers in graphene in the presence of spin-polarized charged impurities by calculating the time evolution of initially polarized state. The spin relaxation time shows completely different energy behaviour for short-ranged and long-ranged spin scatterers and can be used to identify the dominant source of spin scattering. Our results agree well with recent experimental findings and indicate that their spin relaxation is likely caused by long-ranged scatterers. △ Less

Submitted 12 October, 2016; originally announced October 2016.

Comments: 5 pages, 4 figures

Journal ref: Phys. Rev. B 95, 041401 (2017)

Efficient molecular dynamics simulations with many-body potentials on graphics processing units

Authors: Zheyong Fan, Wei Chen, Ville Vierimaa, Ari Harju

Abstract: Graphics processing units have been extensively used to accelerate classical molecular dynamics simulations. However, there is much less progress on the acceleration of force evaluations for many-body potentials compared to pairwise ones. In the conventional force evaluation algorithm for many-body potentials, the force, virial stress, and heat current for a given atom are accumulated within diffe… ▽ More Graphics processing units have been extensively used to accelerate classical molecular dynamics simulations. However, there is much less progress on the acceleration of force evaluations for many-body potentials compared to pairwise ones. In the conventional force evaluation algorithm for many-body potentials, the force, virial stress, and heat current for a given atom are accumulated within different loops, which could result in write conflict between different threads in a CUDA kernel. In this work, we provide a new force evaluation algorithm, which is based on an explicit pairwise force expression for many-body potentials derived recently [Phys. Rev. B 92 (2015) 094301]. In our algorithm, the force, virial stress, and heat current for a given atom can be accumulated within a single thread and is free of write conflicts. We discuss the formulations and algorithms and evaluate their performance. A new open-source code, GPUMD, is developed based on the proposed formulations. For the Tersoff many-body potential, the double precision performance of GPUMD using a Tesla K40 card is equivalent to that of the LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator) molecular dynamics code running with about 100 CPU cores (Intel Xeon CPU X5670 @ 2.93 GHz). △ Less

Submitted 25 June, 2017; v1 submitted 11 October, 2016; originally announced October 2016.

Comments: 8 pages, 4 figures

Journal ref: Comput. Phys. Commun. 218, 10 (2017)

Band geometry, Berry curvature and superfluid weight

Authors: Long Liang, Tuomas I. Vanhala, Sebastiano Peotta, Topi Siro, Ari Harju, Päivi Törmä

Abstract: We present a theory of the superfluid weight in multiband attractive Hubbard models within the Bardeen-Cooper-Schrieffer (BCS) mean field framework. We show how to separate the geometric contribution to the superfluid weight from the conventional one, and that the geometric contribution is associated with the interband matrix elements of the current operator. Our theory can be applied to systems w… ▽ More We present a theory of the superfluid weight in multiband attractive Hubbard models within the Bardeen-Cooper-Schrieffer (BCS) mean field framework. We show how to separate the geometric contribution to the superfluid weight from the conventional one, and that the geometric contribution is associated with the interband matrix elements of the current operator. Our theory can be applied to systems with or without time reversal symmetry. In both cases the geometric superfluid weight can be related to the quantum metric of the corresponding noninteracting systems. This leads to a lower bound on the superfluid weight given by the absolute value of the Berry curvature. We apply our theory to the attractive Kane-Mele-Hubbard and Haldane-Hubbard models, which can be realized in ultracold atom gases. Quantitative comparisons are made to state of the art dynamical mean-field theory and exact diagonalization results. △ Less

Submitted 11 January, 2017; v1 submitted 6 October, 2016; originally announced October 2016.

Comments: Updated version, 17 pages, 10 figures

Journal ref: Phys. Rev. B 95, 024515 (2017)

Single- and many-particle description of scanning tunneling spectroscopy

Authors: Mikko M. Ervasti, Fabian Schulz, Peter Liljeroth, Ari Harju

Abstract: Scanning tunneling spectroscopy measures how a single electron with definite energy propagates between a sample surface and the tip of a scanning tunneling microscope. In the simplest description, the differential conductance measured is interpreted as the local density of states of the sample at the tip position. This picture, however, is insufficient in some cases, since especially smaller molec… ▽ More Scanning tunneling spectroscopy measures how a single electron with definite energy propagates between a sample surface and the tip of a scanning tunneling microscope. In the simplest description, the differential conductance measured is interpreted as the local density of states of the sample at the tip position. This picture, however, is insufficient in some cases, since especially smaller molecules weakly coupled with the substrate tend to have strong Coulomb interactions when an electron is inserted or removed at the molecule. We present theoretical approaches to go from the non-interacting and single-particle picture to the correlated many-body regime. The methodology is used to understand recent experiments on finite armchair graphene nanoribbons and phthalocyanines. We also theoretically discuss the strongly-correlated model system of fractional quantum Hall droplets. △ Less

Submitted 1 July, 2016; originally announced July 2016.

Comments: Submitted to Journal of Electron Spectroscopy and Related Phenomena

Journal ref: J. Electron. Spectrosc. Relat. Phenom. 219, 63-71 (2017)

Multiscale modeling of polycrystalline graphene: A comparison of structure and defect energies of realistic samples from phase field crystal models

Authors: Petri Hirvonen, Mikko M. Ervasti, Zheyong Fan, Morteza Jalalvand, Matthew Seymour, S. Mehdi Vaez Allaei, Nikolas Provatas, Ari Harju, Ken R. Elder, Tapio Ala-Nissila

Abstract: We extend the phase field crystal (PFC) framework to quantitative modeling of polycrystalline graphene. PFC modeling is a powerful multiscale method for finding the ground state configurations of large realistic samples that can be further used to study their mechanical, thermal or electronic properties. By fitting to quantum-mechanical density functional theory (DFT) calculations, we show that th… ▽ More We extend the phase field crystal (PFC) framework to quantitative modeling of polycrystalline graphene. PFC modeling is a powerful multiscale method for finding the ground state configurations of large realistic samples that can be further used to study their mechanical, thermal or electronic properties. By fitting to quantum-mechanical density functional theory (DFT) calculations, we show that the PFC approach is able to predict realistic formation energies and defect structures of grain boundaries. We provide an in-depth comparison of the formation energies between PFC, DFT and molecular dynamics (MD) calculations. The DFT and MD calculations are initialized using atomic configurations extracted from PFC ground states. Finally, we use the PFC approach to explicitly construct large realistic polycrystalline samples and characterize their properties using MD relaxation to demonstrate their quality. △ Less

Submitted 22 June, 2016; v1 submitted 12 May, 2016; originally announced May 2016.

Comments: 18 pages, 15 figures

Dominant source of disorder in graphene: Charged impurities or ripples?

Authors: Zheyong Fan, Andreas Uppstu, Ari Harju

Abstract: Experimentally produced graphene sheets exhibit a wide range of mobility values. Both extrinsic charged impurities and intrinsic ripples (corrugations) have been suggested to induce long-range disorder in graphene and could be a candidate for the dominant source of disorder. Here, using large-scale molecular dynamics and quantum transport simulations, we find that the hopping disorder and the gaug… ▽ More Experimentally produced graphene sheets exhibit a wide range of mobility values. Both extrinsic charged impurities and intrinsic ripples (corrugations) have been suggested to induce long-range disorder in graphene and could be a candidate for the dominant source of disorder. Here, using large-scale molecular dynamics and quantum transport simulations, we find that the hopping disorder and the gauge and scalar potentials induced by the ripples are short-ranged, in strong contrast with predictions by continuous models, and the transport fingerprints of the ripple disorder are very different from those of charged impurities. We conclude that charged impurities are the dominant source of disorder in most graphene samples, whereas scattering by ripples is mainly relevant in the high carrier density limit of ultraclean graphene samples (with a charged impurity concentration < 10 ppm) at room and higher temperatures. △ Less

Submitted 12 May, 2016; originally announced May 2016.

Topological phase transitions in the repulsively interacting Haldane-Hubbard model

Authors: Tuomas I. Vanhala, Topi Siro, Long Liang, Matthias Troyer, Ari Harju, Päivi Törmä

Abstract: Using dynamical mean-field theory and exact diagonalization we study the phase diagram of the repulsive Haldane-Hubbard model, varying the interaction strength and the sublattice potential difference. In addition to the quantum Hall phase with Chern number $C=2$ and the band insulator with $C=0$ present already in the noninteracting model, the system also exhibits a $C=0$ Mott insulating phase, an… ▽ More Using dynamical mean-field theory and exact diagonalization we study the phase diagram of the repulsive Haldane-Hubbard model, varying the interaction strength and the sublattice potential difference. In addition to the quantum Hall phase with Chern number $C=2$ and the band insulator with $C=0$ present already in the noninteracting model, the system also exhibits a $C=0$ Mott insulating phase, and a $C=1$ quantum Hall phase. We explain the latter phase by a spontaneous symmetry breaking where one of the spin-components is in the Hall state and the other in the band insulating state. △ Less

Submitted 25 April, 2016; v1 submitted 29 December, 2015; originally announced December 2015.

Comments: Updated version, 6 pages, 4 figures

Journal ref: Phys. Rev. Lett. 116, 225305 (2016)

Exact diagonalization of quantum lattice models on coprocessors

Authors: Topi Siro, Ari Harju

Abstract: We implement the Lanczos algorithm on an Intel Xeon Phi coprocessor and compare its performance to a multi-core Intel Xeon CPU and an NVIDIA graphics processor. The Xeon and the Xeon Phi are parallelized with OpenMP and the graphics processor is programmed with CUDA. The performance is evaluated by measuring the execution time of a single step in the Lanczos algorithm. We study two quantum lattice… ▽ More We implement the Lanczos algorithm on an Intel Xeon Phi coprocessor and compare its performance to a multi-core Intel Xeon CPU and an NVIDIA graphics processor. The Xeon and the Xeon Phi are parallelized with OpenMP and the graphics processor is programmed with CUDA. The performance is evaluated by measuring the execution time of a single step in the Lanczos algorithm. We study two quantum lattice models with different particle numbers, and conclude that for small systems, the multi-core CPU is the fastest platform, while for large systems, the graphics processor is the clear winner, reaching speedups of up to 7.6 compared to the CPU. The Xeon Phi outperforms the CPU with sufficiently large particle number, reaching a speedup of 2.5. △ Less

Submitted 24 May, 2016; v1 submitted 3 November, 2015; originally announced November 2015.

Silicon and silicon-nitrogen impurities in graphene: structure, energetics and effects on electronic transport

Authors: Mikko M. Ervasti, Zheyong Fan, Andreas Uppstu, Arkady Krasheninnikov, Ari Harju

Abstract: We theoretically study the atomic structure and energetics of silicon and silicon-nitrogen impurities in graphene. Using density-functional theory, we get insight into the atomic structures of the impurities, evaluate their formation energies and assess their abundance in realistic samples. We find that nitrogen, as well as oxygen and hydrogen, are trapped at silicon impurities, considerably alter… ▽ More We theoretically study the atomic structure and energetics of silicon and silicon-nitrogen impurities in graphene. Using density-functional theory, we get insight into the atomic structures of the impurities, evaluate their formation energies and assess their abundance in realistic samples. We find that nitrogen, as well as oxygen and hydrogen, are trapped at silicon impurities, considerably altering the electronic properties of the system. Furthermore, we show that nitrogen doping can induce local magnetic moments resulting in spin-dependent transport properties, even though neither silicon nor nitrogen impurities are magnetic by themselves. To simulate large systems with many randomly distributed impurities, we derive tight-binding models that describe the effects of the impurities on graphene π electron structure. Then by using the linear-scaling real-space Kubo-Greenwood method, we evaluate the transport properties of large-scale systems with random distribution of impurities, and find the fingerprint-like scattering cross sections for each impurity type. The transport properties vary widely, and our results indicate that some of the impurities can even induce strong localization in realistic graphene samples. △ Less

Submitted 31 August, 2015; originally announced September 2015.

Comments: 17 pages, 9 figures

Scaling behavior of spin transport in hydrogenated graphene

Authors: M. R. Thomsen, M. Ervasti, A. Harju, T. G. Pedersen

Abstract: We calculate the spin transport of hydrogenated graphene using the Landauer-Büttiker formalism with a spin-dependent tight-binding Hamiltonian. The advantages of using this method is that it simultaneously gives information on sheet resistance and localization length as well as spin relaxation length. Furthermore, the Landauer-Büttiker formula can be computed very efficiently using the recursive G… ▽ More We calculate the spin transport of hydrogenated graphene using the Landauer-Büttiker formalism with a spin-dependent tight-binding Hamiltonian. The advantages of using this method is that it simultaneously gives information on sheet resistance and localization length as well as spin relaxation length. Furthermore, the Landauer-Büttiker formula can be computed very efficiently using the recursive Green's function technique. Previous theoretical results on spin relaxation time in hydrogenated graphene have not been in agreement with experiments. Here, we study magnetic defects in graphene with randomly aligned magnetic moments, where interference between spin-channels is explicitly included. We show that the spin relaxation length and sheet resistance scale nearly linearly with the impurity concentration. Moreover, the spin relaxation mechanism in hydrogenated graphene is Markovian only near the charge neutrality point or in the highly dilute impurity limit. △ Less

Submitted 17 July, 2015; originally announced July 2015.

Journal ref: Phys. Rev. B 92, 195408 (2015)

Force and heat current formulas for many-body potentials in molecular dynamics simulation with applications to thermal conductivity calculations

Authors: Zheyong Fan, Luiz Felipe C. Pereira, Hui-Qiong Wang, Jin-Cheng Zheng, Davide Donadio, Ari Harju

Abstract: We derive expressions of interatomic force and heat current for many-body potentials such as the Tersoff, the Brenner, and the Stillinger-Weber potential used extensively in molecular dynamics simulations of covalently bonded materials. Although these potentials have a many-body nature, a pairwise force expression that follows Newton's third law can be found without referring to any partition of t… ▽ More We derive expressions of interatomic force and heat current for many-body potentials such as the Tersoff, the Brenner, and the Stillinger-Weber potential used extensively in molecular dynamics simulations of covalently bonded materials. Although these potentials have a many-body nature, a pairwise force expression that follows Newton's third law can be found without referring to any partition of the potential. Based on this force formula, a stress applicable for periodic systems can be unambiguously defined. The force formula can then be used to derive the heat current formulas using a natural potential partitioning. Our heat current formulation is found to be equivalent to most of the seemingly different heat current formulas used in the literature, but to deviate from the stress-based formula derived from two-body potential. We validate our formulation numerically on various systems descried by the Tersoff potential, namely three-dimensional silicon and diamond, two-dimensional graphene, and quasi-one-dimensional carbon nanotube. The effects of cell size and time used in the simulation are examined. △ Less

Submitted 23 March, 2015; originally announced March 2015.

Comments: 14 pages, 6 figures

Journal ref: Phys. Rev. B 92, 094301 (2015)

Validity of the single-particle description and charge noise resilience for multielectron quantum dots

Authors: Michiel A. Bakker, Sebastian Mehl, Tuukka Hiltunen, Ari Harju, David P. DiVincenzo

Abstract: We construct an optimal set of single-particle states for few-electron quantum dots (QDs) using the method of natural orbitals (NOs). The NOs include also the effects of the Coulomb repulsion between electrons. We find that they agree well with the noniteracting orbitals for GaAs QDs of realistic parameters, while the Coulomb interactions only rescale the radius of the NOs compared to the noninter… ▽ More We construct an optimal set of single-particle states for few-electron quantum dots (QDs) using the method of natural orbitals (NOs). The NOs include also the effects of the Coulomb repulsion between electrons. We find that they agree well with the noniteracting orbitals for GaAs QDs of realistic parameters, while the Coulomb interactions only rescale the radius of the NOs compared to the noninteracting case. We use NOs to show that four-electron QDs are less susceptible to charge noise than their two-electron counterparts. △ Less

Submitted 22 April, 2015; v1 submitted 11 February, 2015; originally announced February 2015.

Comments: 11+ pages, 5 figures

Journal ref: Phys. Rev. B 91, 155425 (2015)

Electronic and transport properties in geometrically disordered graphene antidot lattices

Authors: Zheyong Fan, Andreas Uppstu, Ari Harju

Abstract: A graphene antidot lattice, created by a regular perforation of a graphene sheet, can exhibit a considerable band gap required by many electronics devices. However, deviations from perfect periodicity are always present in real experimental setups and can destroy the band gap. Our numerical simulations, using an efficient linear-scaling quantum transport simulation method implemented on graphics p… ▽ More A graphene antidot lattice, created by a regular perforation of a graphene sheet, can exhibit a considerable band gap required by many electronics devices. However, deviations from perfect periodicity are always present in real experimental setups and can destroy the band gap. Our numerical simulations, using an efficient linear-scaling quantum transport simulation method implemented on graphics processing units, show that disorder that destroys the band gap can give rise to a transport gap caused by Anderson localization. The size of the defect induced transport gap is found to be proportional to the radius of the antidots and inversely proportional to the square of the lattice periodicity. Furthermore, randomness in the positions of the antidots is found to be more detrimental than randomness in the antidot radius. The charge carrier mobilities are found to be very small compared to values found in pristine graphene, in accordance with recent experiments. △ Less

Submitted 22 December, 2014; v1 submitted 19 December, 2014; originally announced December 2014.

Comments: 8 pages, 8 figures, An unused figure from the previous version is removed

Journal ref: Phys. Rev. B 91, 125434 (2015)

Charge-noise tolerant exchange gates of singlet-triplet qubits in asymmetric double quantum dots

Authors: Tuukka Hiltunen, Hendrik Bluhm, Sebastian Mehl, Ari Harju

Abstract: In the semi-conductor double quantum dot singlet-triplet qubit architecture, the decoherence caused by the qubit's charge environment poses a serious obstacle in the way towards large scale quantum computing. The effects of the charge decoherence can be mitigated by operating the qubit in the so called sweet spot regions where it is insensitive to electrical noise. In this paper, we propose single… ▽ More In the semi-conductor double quantum dot singlet-triplet qubit architecture, the decoherence caused by the qubit's charge environment poses a serious obstacle in the way towards large scale quantum computing. The effects of the charge decoherence can be mitigated by operating the qubit in the so called sweet spot regions where it is insensitive to electrical noise. In this paper, we propose singlet-triplet qubits based on two quantum dots of different sizes. Such asymmetric double dot systems allow the implementation of exchange gates with controllable exchange splitting $J$ operated in the doubly occupied charge region of the larger dot, where the qubit has high resilience to charge noise. In the larger dot, $J$ can be quenched to a value smaller than the intra-dot tunneling using magnetic fields, while the smaller dot and its larger splitting can be used in the projective readout of the qubit. △ Less

Submitted 4 December, 2014; originally announced December 2014.

Superfluidity and Density Order in a Bilayer Extended Hubbard Model

Authors: Tuomas I. Vanhala, Jildou E. Baarsma, Miikka O. J. Heikkinen, Matthias Troyer, Ari Harju, Päivi Törmä

Abstract: We use cluster dynamical mean field theory to study the phase diagram of the square lattice bilayer Hubbard model with an interlayer interaction. The layers are populated by two-component fermions, and the densities in both layers and the strength of the interactions are varied. We find that an attractive interlayer interaction can induce a checkerboard density ordered phase and superfluid phases,… ▽ More We use cluster dynamical mean field theory to study the phase diagram of the square lattice bilayer Hubbard model with an interlayer interaction. The layers are populated by two-component fermions, and the densities in both layers and the strength of the interactions are varied. We find that an attractive interlayer interaction can induce a checkerboard density ordered phase and superfluid phases, with either interlayer or intralayer pairing. Remarkably, the latter phase does not require an intralayer interaction to be present: it can be attributed to an induced attractive interaction caused by density fluctuations in the other layer. △ Less

Submitted 20 April, 2016; v1 submitted 13 November, 2014; originally announced November 2014.

Comments: The published version

Journal ref: Phys. Rev. B 91, 144510 (2015)

Impurities and Landau level mixing in a fractional quantum Hall state in a flatband lattice model

Authors: Topi Siro, Mikko Ervasti, Ari Harju

Abstract: We study the toplogical checkerboard lattice model around the $ν=\frac{1}{3}$ fractional quantum Hall phase using numerical exact diagonalization without Landau level projections. We add local perturbations, modified hoppings and on-site potentials, and observe phase transitions from the fractional quantum Hall phase to metallic and insulating phases when the strength and number of impurities is i… ▽ More We study the toplogical checkerboard lattice model around the $ν=\frac{1}{3}$ fractional quantum Hall phase using numerical exact diagonalization without Landau level projections. We add local perturbations, modified hoppings and on-site potentials, and observe phase transitions from the fractional quantum Hall phase to metallic and insulating phases when the strength and number of impurities is increased. In addition to evaluating the energy spectrum, we identify the phase diagrams by computing the topological Chern number of the many-body ground state manifold, and we show how the ground states lose their correlations due to the impurities by evaluating the spectrum of the one-body reduced density matrix. Our results show that the phase transition from the fractional quantum Hall phase to the metallic phase occurs for both impurity hoppings and potentials. Strong impurity hoppings cause a further transition into the insulating state, regardless of the sign of the hopping, when their density is high enough. In contrast, the same happens only for attractive potentials. Furthermore, the mixing to the higher band in a two-band model, generally denoted as Landau level mixing, is measured concluding that the lowest Landau level projection works well even with remarkably strong interactions and in the presence of impurities. △ Less

Submitted 7 October, 2014; v1 submitted 9 May, 2014; originally announced May 2014.

Journal ref: Phys. Rev. B 90 (2014), 165101

Capacitative coupling of singlet-triplet qubits in different inter-qubit geometries

Authors: Tuukka Hiltunen, Ari Harju

Abstract: In the singlet-triplet qubit architecture, the two-qubit interactions required in universal quantum computing can be implemented by capacitative coupling, by exploiting the charge distribution differences of the singlet and triplet states. The efficiency of this scheme is limited by decoherence, that can be mitigated by stronger coupling between the qubits. In this paper, we study the capacitative… ▽ More In the singlet-triplet qubit architecture, the two-qubit interactions required in universal quantum computing can be implemented by capacitative coupling, by exploiting the charge distribution differences of the singlet and triplet states. The efficiency of this scheme is limited by decoherence, that can be mitigated by stronger coupling between the qubits. In this paper, we study the capacitative coupling of singlet-triplet qubits in different geometries of the two-qubit system. The effects of the qubit-qubit distance and the relative orientation of the qubits on the capacitative coupling strength are discussed using an accurate microscopic model and exact diagonalization of it. We find that the trapezoidal quantum dot formations allow strong coupling with low charge distribution differences between the singlet and triplet states. The analysis of geometry on the capacitative coupling is also extended to the many-qubit case and the creation of cluster states. △ Less

Submitted 22 April, 2014; originally announced April 2014.

Self-consistent energy approximation for orbital-free density-functional theory

Authors: E. Rasanen, A. Odriazola, I. Makkonen, A. Harju

Abstract: Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation and yields the total energy and density as a function of the external potential, the number of electrons, and the chemical potential determined upon normalizatio… ▽ More Employing a local formula for the electron-electron interaction energy, we derive a self-consistent approximation for the total energy of a general $N$-electron system. Our scheme works as a local variant of the Thomas-Fermi approximation and yields the total energy and density as a function of the external potential, the number of electrons, and the chemical potential determined upon normalization. Our tests for Hooke's atoms, jellium, and model atoms up to $\sim 1000$ electrons show that reasonable total energies can be obtained with almost a negligible computational cost. The results are also consistent in the important large-$N$ limit. △ Less

Submitted 30 October, 2013; originally announced October 2013.

Anderson localization in two-dimensional graphene with short-range disorder: One-parameter scaling and finite-size effects

Authors: Zheyong Fan, Andreas Uppstu, Ari Harju

Abstract: We study Anderson localization in graphene with short-range disorder using the real-space Kubo-Greenwood method implemented on graphics processing units. Two models of short-range disorder, namely, the Anderson on-site disorder model and the vacancy defect model, are considered. For graphene with Anderson disorder, localization lengths of quasi-one-dimensional systems with various disorder strengt… ▽ More We study Anderson localization in graphene with short-range disorder using the real-space Kubo-Greenwood method implemented on graphics processing units. Two models of short-range disorder, namely, the Anderson on-site disorder model and the vacancy defect model, are considered. For graphene with Anderson disorder, localization lengths of quasi-one-dimensional systems with various disorder strengths, edge symmetries, and boundary conditions are calculated using the real-space Kubo-Greenwood formalism, showing excellent agreement with independent transfer matrix calculations and superior computational efficiency. Using these data, we demonstrate the applicability of the one-parameter scaling theory of localization length and propose an analytical expression for the scaling function, which provides a reliable method of computing the two-dimensional localization length. This method is found to be consistent with another widely used method which relates the two-dimensional localization length to the elastic mean free path and the semiclassical conductivity. Abnormal behavior at the charge neutrality point is identified and interpreted to be caused by finite-size effects when the system width is comparable to or smaller than the elastic mean free path. We also demonstrate the finite-size effect when calculating the two-dimensional conductivity in the localized regime and show that a renormalization group beta function consistent with the one-parameter scaling theory can be extracted numerically. For graphene with vacancy disorder, we show that the proposed scaling function of localization length also applies. Lastly, we discuss some ambiguities in calculating the semiclassical conductivity around the charge neutrality point due to the presence of resonant states. △ Less

Submitted 30 June, 2014; v1 submitted 30 October, 2013; originally announced October 2013.

Comments: 15 pages, 14 figures

Journal ref: Phys. Rev. B 89, 245422 (2014)

Obtaining localization properties efficiently using the Kubo-Greenwood formalism

Authors: Andreas Uppstu, Zheyong Fan, Ari Harju

Abstract: We establish, through numerical calculations and comparisons with a recursive Green's function based implementation of the Landauer-Büttiker formalism, an efficient method for studying Anderson localization in quasi-one-dimensional and two-dimensional systems using the Kubo-Greenwood formalism. Although the recursive Green's function method can be used to obtain the localization length of a mesosc… ▽ More We establish, through numerical calculations and comparisons with a recursive Green's function based implementation of the Landauer-Büttiker formalism, an efficient method for studying Anderson localization in quasi-one-dimensional and two-dimensional systems using the Kubo-Greenwood formalism. Although the recursive Green's function method can be used to obtain the localization length of a mesoscopic conductor, it is numerically very expensive for systems that contain a large number of atoms transverse to the transport direction. On the other hand, linear-scaling has been achieved with the Kubo-Greenwood method, enabling the study of effectively two-dimensional systems. While the propagating length of the charge carriers will eventually saturate to a finite value in the localized regime, the conductances given by the Kubo-Greenwood method and the recursive Green's function method agree before the saturation. The converged value of the propagating length is found to be directly proportional to the localization length obtained from the exponential decay of the conductance. △ Less

Submitted 24 February, 2014; v1 submitted 28 October, 2013; originally announced October 2013.

Comments: 7 pages, 6 figures

Journal ref: Phys. Rev. B 89, 075420 (2014)

Maximal tripartite entanglement between singlet-triplet qubits in quantum dots

Authors: Tuukka Hiltunen, Ari Harju

Abstract: Singlet-triplet states in double quantum dots are promising realizations of qubits, and capacitive coupling can be used to create entanglement between these qubits. We propose an entangling three-qubit gate of singlet-triplet qubits in a triangular setup. Our simulations using a realistic microscopic model show that a maximally entangled Greenberger-Horne-Zeilinger state can be generated as the qu… ▽ More Singlet-triplet states in double quantum dots are promising realizations of qubits, and capacitive coupling can be used to create entanglement between these qubits. We propose an entangling three-qubit gate of singlet-triplet qubits in a triangular setup. Our simulations using a realistic microscopic model show that a maximally entangled Greenberger-Horne-Zeilinger state can be generated as the qubits are evolved under exchange. Furthermore, our analysis for the gate operation can be used to extract the actual experimental pulse sequence needed to realize this. △ Less

Submitted 24 October, 2013; v1 submitted 27 September, 2013; originally announced September 2013.

Non-adiabatic charge state transitions in singlet-triplet qubits

Authors: Tuukka Hiltunen, Juha Ritala, Topi Siro, Ari harju

Abstract: In double quantum dot singlet-triplet qubits, the exchange interaction is used in both quantum gate operation and the measurement of the state of the qubit. The exchange can be controlled electronically by applying gate voltage pulses. We simulate the exchange induced charge state transitions in one and two singlet-triplet qubit systems using the exact diagonalization method. We find that fast det… ▽ More In double quantum dot singlet-triplet qubits, the exchange interaction is used in both quantum gate operation and the measurement of the state of the qubit. The exchange can be controlled electronically by applying gate voltage pulses. We simulate the exchange induced charge state transitions in one and two singlet-triplet qubit systems using the exact diagonalization method. We find that fast detuning pulses may result in leakage between different singlet charge states. The leakage could cause measurement errors and hinder quantum gate operation for example in the case of the two-qubit Coulomb gate. △ Less

Submitted 26 September, 2013; originally announced September 2013.

Journal ref: 2013 New J. Phys. 15 103015

Enhancement models of momentum densities of annihilating electron-positron pairs: the many-body picture of natural geminals

Authors: Ilja Makkonen, Mikko M. Ervasti, Topi Siro, Ari Harju

Abstract: The correlated motion of a positron surrounded by electrons is a fundamental many-body problem. We approach this by modeling the momentum density of annihilating electron-positron pairs using the framework of reduced density matrices, natural orbitals and natural geminals (electron-positron pair wave functions) of the quantum theory of many-particle systems. We find that an expression based on the… ▽ More The correlated motion of a positron surrounded by electrons is a fundamental many-body problem. We approach this by modeling the momentum density of annihilating electron-positron pairs using the framework of reduced density matrices, natural orbitals and natural geminals (electron-positron pair wave functions) of the quantum theory of many-particle systems. We find that an expression based on the natural geminals provides an exact, unique and compact expression for the momentum density. The natural geminals can be used to define and determine enhancement factors for enhancement models going beyond the independent-particle model for a better understanding of results of positron annihilation experiments. △ Less

Submitted 19 December, 2013; v1 submitted 26 September, 2013; originally announced September 2013.

Comments: Resubmitted to Physical Review B (Rapid Communications) on 19 December 2013

Journal ref: Physical Review B 89, 041105(R) (2014)

Efficient linear-scaling quantum transport calculations on graphics processing units and applications on electron transport in graphene

Authors: Zheyong Fan, Andreas Uppstu, Topi Siro, Ari Harju

Abstract: We implement, optimize, and validate the linear-scaling Kubo-Greenwood quantum transport simulation on graphics processing units by examining resonant scattering in graphene. We consider two practical representations of the Kubo-Greenwood formula: a Green-Kubo formula based on the velocity auto-correlation and an Einstein formula based on the mean square displacement. The code is fully implemented… ▽ More We implement, optimize, and validate the linear-scaling Kubo-Greenwood quantum transport simulation on graphics processing units by examining resonant scattering in graphene. We consider two practical representations of the Kubo-Greenwood formula: a Green-Kubo formula based on the velocity auto-correlation and an Einstein formula based on the mean square displacement. The code is fully implemented on graphics processing units with a speedup factor of up to 16 (using double-precision) relative to our CPU implementation. We compare the kernel polynomial method and the Fourier transform method for the approximation of the Dirac delta function and conclude that the former is more efficient. In the ballistic regime, the Einstein formula can produce the correct quantized conductance of one-dimensional graphene nanoribbons except for an overshoot near the band edges. In the diffusive regime, the Green-Kubo and the Einstein formalisms are demonstrated to be equivalent. A comparison of the length-dependence of the conductance in the localization regime obtained by the Einstein formula with that obtained by the non-equilibrium Green's function method reveals the challenges in defining the length in the Kubo-Greenwood formalism at the strongly localized regime. △ Less

Submitted 1 July, 2013; originally announced July 2013.

Comments: 15 pages, 8 figures

Journal ref: Computer Physics Communications, Volume 185, Issue 1, January 2014, Pages 28-39

Electronic states in finite graphene nanoribbons: Effect of charging and defects

Authors: M. Ijäs, M. Ervasti, A. Uppstu, P. Liljeroth, J. van der Lit, I. Swart, A. Harju

Abstract: We study the electronic structure of finite armchair graphene nanoribbons using density-functional theory and the Hubbard model, concentrating on the states localized at the zigzag termini. We show that the energy gaps between end-localized states are sensitive to doping, and that in doped systems, the gap between the end-localized states decreases exponentially as a function of the ribbon length.… ▽ More We study the electronic structure of finite armchair graphene nanoribbons using density-functional theory and the Hubbard model, concentrating on the states localized at the zigzag termini. We show that the energy gaps between end-localized states are sensitive to doping, and that in doped systems, the gap between the end-localized states decreases exponentially as a function of the ribbon length. Doping also quenches the antiferromagnetic coupling between the end-localized states leading to a spin-split gap in neutral ribbons. By comparing dI/dV maps calculated using the many-body Hubbard model, its mean-field approximation and density-functional theory, we show that the use of a single-particle description is justified for graphene π states. Furthermore, we study the effect of structural defects in the ribbons on their electronic structure. Defects at one ribbon termini do not significantly modify the electronic states localized at the intact end. This provides further evidence for the interpretation of a multi-peaked structure in a recent scanning tunneling spectroscopy (STS) experiment resulting from inelastic tunneling processes [J. van der Lit et al., Nature Commun., in press (2013)]. Finally, we show that the hydrogen termination at the flake edges leaves identifiable fingerprints on the positive bias side of STS measurements, thus possibly aiding the experimental identification of graphene structures. △ Less

Submitted 12 June, 2013; originally announced June 2013.

Journal ref: Phys. Rev. B 88, 075429 (2013)

Single- and multi-mode Fabry-Pérot interference in suspended graphene

Authors: Mika Oksanen, Andreas Uppstu, Antti Laitinen, Daniel J. Cox, Monica Craciun, Saverio Russo, Ari Harju, Pertti Hakonen

Abstract: Phase coherence of charge carriers leads to electron-wave interference in ballistic mesoscopic conductors. In graphene, such Fabry-Pérot-like interference has been observed, but a detailed analysis has been complicated by the two-dimensional nature of conduction, which allows for complex interference patterns. In this work, we have achieved high-quality Fabry-Pérot interference in a suspended grap… ▽ More Phase coherence of charge carriers leads to electron-wave interference in ballistic mesoscopic conductors. In graphene, such Fabry-Pérot-like interference has been observed, but a detailed analysis has been complicated by the two-dimensional nature of conduction, which allows for complex interference patterns. In this work, we have achieved high-quality Fabry-Pérot interference in a suspended graphene device, both in conductance and in shot noise, and analyzed their structure using Fourier transform techniques. The Fourier analysis reveals two sets of overlapping, coexisting interferences, with the ratios of the diamonds being equal to the width to length ratio of the device. We attribute these sets to a unique coexistence of longitudinal and transverse resonances, with the longitudinal resonances originating from the bunching of modes with low transverse momentum. Furthermore, our results give insight into the renormalization of the Fermi velocity in suspended graphene samples, caused by unscreened many-body interactions. △ Less

Submitted 5 June, 2013; originally announced June 2013.

Comments: 6 pages, 3 figures

Journal ref: Phys. Rev. B 89, 121414(R) (2014)

Interaction of chlorine with Stone-Wales de- fects in graphene and carbon nanotubes, and thermodynamical prospects of chlorine-induced nanotube unzipping

Authors: M. Ijäs, P. Havu, A. Harju

Abstract: We study the binding of chlorine atoms to carbon nanotubes and graphene at a Stone-Wales defect and to the sidewalls of pristine nanotubes. We show using ab initio thermodynamics that if the environment is chlorine-rich enough, the unzipping of carbon nanotubes into graphene nanoribbons with chlorinated edges may be thermodynamically feasible. By controlling the Cl chemical potential through tempe… ▽ More We study the binding of chlorine atoms to carbon nanotubes and graphene at a Stone-Wales defect and to the sidewalls of pristine nanotubes. We show using ab initio thermodynamics that if the environment is chlorine-rich enough, the unzipping of carbon nanotubes into graphene nanoribbons with chlorinated edges may be thermodynamically feasible. By controlling the Cl chemical potential through temperature and pressure, opening selectively tubes below a threshold diameter might be possible. Additionally, we find increased binding energies for chlorine atoms bound to Stone-Wales defects as compared to defect-free graphene and nanotubes, indicating that defects might act as nucleation sites for tube unzipping. On graphene, no more than a single Cl atom may be bound to the defect in ambient conditions, limiting possible Cl-induced changes in the resulting nanoribbons. △ Less

Submitted 22 May, 2013; originally announced May 2013.

Journal ref: Phys. Rev. B 87, 205430 (2013)

Lagrange mesh and exact diagonalization for numerical study of semiconductor quantum dot systems with application in singlet-triplet qubits

Authors: Tuukka Hiltunen, Juha Ritala, Oona Kupiainen, Topi Siro, Ari Harju

Abstract: We present a highly flexible computational scheme for studying correlated electrons confined by an arbitrary external potential in two-dimensional semiconductor quantum dots. The method starts by a Lagrange mesh calculation for the single-particle states, followed by the calculation of the Coulomb interaction matrix elements between these, and combining both in the exact diagonalization of the man… ▽ More We present a highly flexible computational scheme for studying correlated electrons confined by an arbitrary external potential in two-dimensional semiconductor quantum dots. The method starts by a Lagrange mesh calculation for the single-particle states, followed by the calculation of the Coulomb interaction matrix elements between these, and combining both in the exact diagonalization of the many-body Hamiltonian. We apply the method in simulation of double quantum dot singlet-triplet qubits. We simulate the full quantum control and dynamics of one singlet-triplet qubit. We also use our method to provide an exact diagonalization based first-principles model for studying two singlet-triplet qubits and their capacitative coupling via the long-distance Coulomb interaction. △ Less

Submitted 28 January, 2013; originally announced January 2013.

Comments: 14 pages, 12 figures

Ab-initio transport fingerprints for resonant scattering in graphene

Authors: Karri Saloriutta, Andreas Uppstu, Ari Harju, Martti J. Puska

Abstract: We have recently shown that by using a scaling approach for randomly distributed topological defects in graphene, reliable estimates for transmission properties of macroscopic samples can be calculated based even on single-defect calculations [A. Uppstu et al., Phys. Rev. B 85, 041401 (2012)]. We now extend this approach of energy-dependent scattering cross sections to the case of adsorbates on gr… ▽ More We have recently shown that by using a scaling approach for randomly distributed topological defects in graphene, reliable estimates for transmission properties of macroscopic samples can be calculated based even on single-defect calculations [A. Uppstu et al., Phys. Rev. B 85, 041401 (2012)]. We now extend this approach of energy-dependent scattering cross sections to the case of adsorbates on graphene by studying hydrogen and carbon adatoms as well as epoxide and hydroxyl groups. We show that a qualitative understanding of resonant scattering can be gained through density functional theory results for a single-defect system, providing a transmission "fingerprint" characterizing each adsorbate type. This information can be used to reliably predict the elastic mean free path for moderate defect densities directly using ab-initio methods. We present tight-binding parameters for carbon and epoxide adsorbates, obtained to match the density-functional theory based scattering cross sections. △ Less

Submitted 30 November, 2012; originally announced November 2012.

Journal ref: Phys. Rev. B 86, 235417 (2012)

Accelerated molecular dynamics force evaluation on graphics processing units for thermal conductivity calculations

Authors: Zheyong Fan, Topi Siro, Ari Harju

Abstract: In this paper, we develop a highly efficient molecular dynamics code fully implemented on graphics processing units for thermal conductivity calculations using the Green-Kubo formula. We compare two different schemes for force evaluation, a previously used thread-scheme where a single thread is used for one particle and each thread calculates the total force for the corresponding particle, and a n… ▽ More In this paper, we develop a highly efficient molecular dynamics code fully implemented on graphics processing units for thermal conductivity calculations using the Green-Kubo formula. We compare two different schemes for force evaluation, a previously used thread-scheme where a single thread is used for one particle and each thread calculates the total force for the corresponding particle, and a new block-scheme where a whole block is used for one particle and each thread in the block calculates one or several pair forces between the particle associated with the given block and its neighbor particle(s) associated with the given thread. For both schemes, two different classical potentials, namely, the Lennard-Jones potential and the rigid-ion potential are implemented. While the thread-scheme performs a little better for relatively large systems, the block-scheme performs much better for relatively small systems. The relative performance of the block-scheme over the thread-scheme also increases with the increasing of the cutoff radius. We validate the implementation by calculating lattice thermal conductivities of solid argon and lead telluride. △ Less

Submitted 13 March, 2013; v1 submitted 16 November, 2012; originally announced November 2012.

Journal ref: Computer Physics Communications, Volume 184, Issue 5, May 2013, Pages 1414-1425

Computational Physics on Graphics Processing Units

Authors: Ari Harju, Topi Siro, Filippo Federici-Canova, Samuli Hakala, Teemu Rantalaiho

Abstract: The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing on classical molecular dynamics, and on quantum simulations for electronic structure calculations using the density functional theory, wave function techniques,… ▽ More The use of graphics processing units for scientific computations is an emerging strategy that can significantly speed up various different algorithms. In this review, we discuss advances made in the field of computational physics, focusing on classical molecular dynamics, and on quantum simulations for electronic structure calculations using the density functional theory, wave function techniques, and quantum field theory. △ Less

Submitted 6 March, 2013; v1 submitted 30 October, 2012; originally announced October 2012.

Comments: Proceedings of the 11th International Conference, PARA 2012, Helsinki, Finland, June 10-13, 2012

Journal ref: Lecture Notes in Computer Science, volume 7782, pp 3-26 (2013). In "Applied Parallel and Scientific Computing", Editors Pekka Manninen and Per Öster

High-temperature surface superconductivity in rhombohedral graphite

Authors: N. B. Kopnin, M. Ijäs, A. Harju, T. T. Heikkilä

Abstract: Surface superconductivity in rhombohedral graphite is a robust phenomenon which can exist even when higher order hoppings between the layers lift the topological protection of the surface flat band and introduce a quadratic dispersion of electrons with a heavy effective mass. We show that for weak pairing interaction, the flat band character of the surface superconductivity transforms into a BCS-l… ▽ More Surface superconductivity in rhombohedral graphite is a robust phenomenon which can exist even when higher order hoppings between the layers lift the topological protection of the surface flat band and introduce a quadratic dispersion of electrons with a heavy effective mass. We show that for weak pairing interaction, the flat band character of the surface superconductivity transforms into a BCS-like relation with high critical temperature characterized by a higher coupling constant due to a much larger density of states than in the bulk. Our results offer an explanation for the recent findings of graphite superconductivity with an unusually high transition temperature. △ Less

Submitted 29 October, 2012; originally announced October 2012.

Comments: 7 pages, 5 figures. Short version of arXiv:1210.7075

Journal ref: Phys. Rev. B 87, 140503(R) (2013)

Scaling in the correlation energies of two-dimensional artificial atoms

Authors: Alexander Odriazola, Mikko M Ervasti, Ilja Makkonen, Alain Delgado, Augusto González, Esa Räsänen, Ari Harju

Abstract: We find an unexpected scaling in the correlation energy of artificial atoms, i.e., harmonically confined two-dimensional quantum dots. The scaling relation is found through extensive numerical examinations including Hartree-Fock, variational quantum Monte Carlo, density-functional, and full configuration-interaction calculations. We show that the correlation energy, i.e., the true ground-state tot… ▽ More We find an unexpected scaling in the correlation energy of artificial atoms, i.e., harmonically confined two-dimensional quantum dots. The scaling relation is found through extensive numerical examinations including Hartree-Fock, variational quantum Monte Carlo, density-functional, and full configuration-interaction calculations. We show that the correlation energy, i.e., the true ground-state total energy subtracted by the Hartree-Fock total energy, follows a simple function of the Coulomb energy, confimenent strength and, the number of electrons. We find an analytic expression for this function, as well as for the correlation energy per particle and for the ratio between the correlation and total energies. Our tests for independent diffusion Monte Carlo and coupled-cluster results for quantum dots -- including open-shell data -- confirm the generality of the obtained scaling. As the scaling is also well applicable to $\gtrsim$ 100 electrons, our results give interesting prospects for the development of correlation functionals within density-functional theory. △ Less

Submitted 22 October, 2013; v1 submitted 6 September, 2012; originally announced September 2012.

Comments: Accepted to Journal of Physics: Condensed Matter

Journal ref: J. Phys.: Condens. Matter 25 (2013) 505504

Y-junction splitting spin states of moving quantum dot

Authors: Tuukka Hiltunen, Ari Harju

Abstract: The development of a working quantum computer utilizing electron spin states as qubits is a major goal for many theorists and experimentalists. The future applications of quantum information technology would also require a reliable method for the transportation of quantum information. A promising such method is the propagation of electrons by a surface acoustic wave (SAW). In this paper, we simula… ▽ More The development of a working quantum computer utilizing electron spin states as qubits is a major goal for many theorists and experimentalists. The future applications of quantum information technology would also require a reliable method for the transportation of quantum information. A promising such method is the propagation of electrons by a surface acoustic wave (SAW). In this paper, we simulate the SAW transfer of two interacting electrons through a Y-shaped junction. Our results show that the singlet and triplet states can be differentiated in the Y-junction by an electrostatic detuning potential, an effect that could be used in for example measuring the state of a two-spin qubit. △ Less

Submitted 4 July, 2012; originally announced July 2012.

Journal ref: Phys. Rev. B 86, 121301(R) (2012)

High-field magnetoresistance revealing scattering mechanisms in graphene

Authors: Andreas Uppstu, Ari Harju

Abstract: We show that the type of charge carrier scattering significantly affects the high-field magnetoresistance of graphene nanoribbons. This effect has potential to be used in identifying the scattering mechanisms in graphene. The results also provide an explanation for the experimentally found, intriguing differences in the behavior of the magnetoresistance of graphene Hall bars placed on different su… ▽ More We show that the type of charge carrier scattering significantly affects the high-field magnetoresistance of graphene nanoribbons. This effect has potential to be used in identifying the scattering mechanisms in graphene. The results also provide an explanation for the experimentally found, intriguing differences in the behavior of the magnetoresistance of graphene Hall bars placed on different substrates. Additionally, our simulations indicate that the peaks in the longitudinal resistance tend to become pinned to fractionally quantized values, as different transport modes have very different scattering properties. △ Less

Submitted 13 September, 2012; v1 submitted 2 May, 2012; originally announced May 2012.

Comments: 4 pages, 3 figures

Journal ref: Phys. Rev. B 86, 201409(R) (2012)

Fractional periodicity of persistent current in coupled quantum rings

Authors: M. Ijäs, A. Harju

Abstract: We study the transmission properties of a few-site Hubbard rings with up to second-nearest neighbor coupling embedded to a ring-shaped lead using exact diagonalization. The approach captures all the correlation effects and enables us to include interactions both in the ring and in the ring-shaped lead, and study on an equal footing weak and strong coupling between the ring and the lead as well as… ▽ More We study the transmission properties of a few-site Hubbard rings with up to second-nearest neighbor coupling embedded to a ring-shaped lead using exact diagonalization. The approach captures all the correlation effects and enables us to include interactions both in the ring and in the ring-shaped lead, and study on an equal footing weak and strong coupling between the ring and the lead as well as asymmetry. In the weakly coupled case, we find fractional periodicity at all electron fillings at sufficiently high Hubbard U, similar to isolated rings. For strongly coupled rings, on the contrary, fractional periodicity is only observed at sufficiently large negative gate voltages and high interaction strengths. This is explained by the formation of a bound correlated state in the ring that is effectively weakly coupled to the lead. △ Less

Submitted 2 May, 2012; originally announced May 2012.

Journal ref: Phys. Rev. B 85, 235120 (2012)

Exact diagonalization of the Hubbard model on graphics processing units

Authors: Topi Siro, Ari Harju

Abstract: We solve the Hubbard model with the exact diagonalization method on a graphics processing unit (GPU). We benchmark our GPU program against a sequential CPU code by using the Lanczos algorithm to solve the ground state energy in two cases: a one-dimensional ring and a two-dimensional square lattice. In the one-dimensional case, we obtain speedups of over 100 and 60 in single and double precision ar… ▽ More We solve the Hubbard model with the exact diagonalization method on a graphics processing unit (GPU). We benchmark our GPU program against a sequential CPU code by using the Lanczos algorithm to solve the ground state energy in two cases: a one-dimensional ring and a two-dimensional square lattice. In the one-dimensional case, we obtain speedups of over 100 and 60 in single and double precision arithmetic, respectively. In the two-dimensional case, the corresponding speedups are over 110 and 70. △ Less

Submitted 19 June, 2012; v1 submitted 16 April, 2012; originally announced April 2012.

Journal ref: Computer Physics Communications 183 (2012) pp. 1884-1889

Exchange-correlation potentials for inhomogeneous electron systems in two dimensions from exact diagonalization: comparison with the local-spin-density approximation

Authors: Ilja Makkonen, Mikko M. Ervasti, Ville Kauppila, Ari Harju

Abstract: We consider electronic exchange and correlation effects in density-functional calculations of two-dimensional systems. Starting from wave function calculations of total energies and electron densities of inhomogeneous model systems, we derive corresponding exchange-correlation potentials and energies. We compare these with predictions of the local-spin-density approximation and discuss its accurac… ▽ More We consider electronic exchange and correlation effects in density-functional calculations of two-dimensional systems. Starting from wave function calculations of total energies and electron densities of inhomogeneous model systems, we derive corresponding exchange-correlation potentials and energies. We compare these with predictions of the local-spin-density approximation and discuss its accuracy. Our data will be useful as reference data in testing, comparing and parametrizing exchange and correlation functionals for two-dimensional electronic systems. △ Less

Submitted 13 April, 2012; v1 submitted 17 January, 2012; originally announced January 2012.

Comments: Submitted to Physical Review B on January 3, 2012. Second revised version submitted on April 13, 2012

Journal ref: Physical Review B 85, 205140 (2012)

Fracturing graphene by chlorination: a theoretical viewpoint

Authors: M. Ijäs, P. Havu, A. Harju

Abstract: Motivated by the recent photochlorination experiment [B. Li et al., ACS Nano 5, 5957 (2011)], we study theoretically the interaction of chlorine with graphene. In previous theoretical studies, covalent binding between chlorine and carbon atoms has been elusive upon adsorption to the graphene basal plane. Interestingly, in their recent experiment, Li et al. interpreted their data in terms of chemic… ▽ More Motivated by the recent photochlorination experiment [B. Li et al., ACS Nano 5, 5957 (2011)], we study theoretically the interaction of chlorine with graphene. In previous theoretical studies, covalent binding between chlorine and carbon atoms has been elusive upon adsorption to the graphene basal plane. Interestingly, in their recent experiment, Li et al. interpreted their data in terms of chemical bonding of chlorine on top of the graphene plane, associated with a change from sp2 to sp3 in carbon hybridization and formation of graphene nanodomains. We study the hypothesis that these domains are actually fractured graphene with chlorinated edges, and compare the energetics of chlorine-containing graphene edge terminations, both in zigzag and armchair directions, to chlorine adsorption onto infinite graphene. Our results indicate that edge chlorination is favored over adsorption in the experimental conditions with radical atomic chlorine and that edge chlorination with sp3-hybridized edge carbons is stable also in ambient conditions. An ab initio thermodynamical analysis shows that the presence of chlorine is able to break the pristine graphene layer. Finally, we discuss the possible effects of the silicon dioxide substrate on the chlorination of graphene. △ Less

Submitted 13 January, 2012; originally announced January 2012.

Journal ref: Phys. Rev. B 85, 035440 (2012)