Showing 1–50 of 95 results for author: Engel, A

Hole concentrations in doped gray α-Sn on InSb and CdTe measured with infrared ellipsometry

Authors: Jaden R. Love, Carlos A. Armenta, Atlantis K. Moses, Haley B. Woolf, Jan Hrabovsky, Stefan Zollner, Aaron N. Engel, Christopher J. Palmstrøm

Abstract: Gray tin (α-Sn) layers with 30 nm thickness were grown on InSb (001) substrates using molecular beam epitaxy. The surface preparation of the substrates was adjusted to achieve either n-type or p-type doping in the α-Sn layer. Fourier-transform infrared ellipsometry was used to find the temperature-dependent dielectric function of the α-Sn layers from 0.03 to 0.8 eV and from 10 to 300 K. Because of… ▽ More Gray tin (α-Sn) layers with 30 nm thickness were grown on InSb (001) substrates using molecular beam epitaxy. The surface preparation of the substrates was adjusted to achieve either n-type or p-type doping in the α-Sn layer. Fourier-transform infrared ellipsometry was used to find the temperature-dependent dielectric function of the α-Sn layers from 0.03 to 0.8 eV and from 10 to 300 K. Because of the inverted band structure of α-Sn, the spectra show a strong absorption peak at 0.45 eV due to transitions from the inverted {Γ_-^7} "electron" valence band to the {Γ_+^8} heavy hole valence band. Applying the Thomas-Reiche-Kuhn f-sum rule, the integrated oscillator strength of this peak was used to calculate the heavy hole concentration as a function of temperature. For a nearly intrinsic α-Sn layer, the heavy hole concentration agrees well with predictions based on degenerate Fermi-Dirac statistics. Deviations from the intrinsic α-Sn carrier concentrations are attributed to substrate surface preparation leading to the diffusion of donor or acceptor ions into the α-Sn layer causing n-type or p-type doping. △ Less

Submitted 16 April, 2026; originally announced April 2026.

Spin-orbit coupling in digital alloyed InGaAs quantum wells

Authors: Jason T. Dong, Yilmaz Gul, Irene Villar Rodriguez, Aaron N. Engel, Connor P. Dempsey, Stuart N. Holmes, Michael Pepper, Christopher J. Palmstrøm

Abstract: Increasing the spin-orbit coupling in InGaAs quantum wells is desirable for applications involving spintronics and topological quantum computing. Digital alloying is an approach towards growing ternary quantum wells that enables asymmetric interfaces and compositional grading in the quantum well, which can potentially modify the spin-orbit coupling in the quantum well. The spin-orbit coupling of t… ▽ More Increasing the spin-orbit coupling in InGaAs quantum wells is desirable for applications involving spintronics and topological quantum computing. Digital alloying is an approach towards growing ternary quantum wells that enables asymmetric interfaces and compositional grading in the quantum well, which can potentially modify the spin-orbit coupling in the quantum well. The spin-orbit coupling of the quantum wells is extracted from beating patterns in the low magnetic field magnetoresistance. Digital alloying is found to modify the spin-orbit coupling by up to 138 meV\textnormalÅ. The changes induced in the spin-orbit coupling can be qualitatively understood as being due to modifications in the interfacial Rashba spin-orbit coupling. △ Less

Submitted 7 July, 2025; originally announced July 2025.

Near-half-metallic state in the half Heusler PtMnSb film on a III-V substrate

Authors: Shinichi Nishihaya, Malcolm J. A. Jardine, Hadass S. Inbar, Aranya Goswami, Jason T. Dong, Aaron N. Engel, Yu-Hao Chang, Connor P. Dempsey, Makoto Hashimoto, Donghui Lu, Noa Marom, Chris J. Palmstrøm

Abstract: The interplay between half-metallic ferromagnetism and spin-orbit coupling within the inversion symmetry-broken structure of half Heuslers provides an ideal platform for various spintronics functionalities. Taking advantage of good lattice matching, it is highly desired to epitaxially integrate promising Heuslers into III-V semiconductor-based devices. PtMnSb is one of the first half Heuslers pred… ▽ More The interplay between half-metallic ferromagnetism and spin-orbit coupling within the inversion symmetry-broken structure of half Heuslers provides an ideal platform for various spintronics functionalities. Taking advantage of good lattice matching, it is highly desired to epitaxially integrate promising Heuslers into III-V semiconductor-based devices. PtMnSb is one of the first half Heuslers predicted to be an above-room-temperature half-metal with large spin orbit coupling, however, its half-metallicity and potential as a spintronics material has remained elusive due to lack of high quality samples. Here we demonstrate epitaxial growth of single crystal PtMnSb(001) film on GaSb(001) substrates using molecular beam epitaxy. Direct observation of the band structure via angle-resolved photoemission spectroscopy and many-body perturbation theory within the quasiparticle self-consistent GW approximation (QPGW) reveal that PtMnSb hosts rather a near-halfmetallic state with both spin bands crossing the Fermi level and with high spin polarization over 90%. Temperature dependence of magnetization also shows an anomalous enhancement below 60 K, which can be associated with the development of such a near-half-metallic state at low temperatures. Epitaxial growth of high crystalline PtMnSb on a III-V paves the way for systematic clarification of its spin transport properties with fine-tuning of strain in heterostructure devices. △ Less

Submitted 16 December, 2024; originally announced December 2024.

Comments: 20 pages, 6 figures

Hybridization gap approaching the two-dimensional limit of topological insulator Bi$_x$Sb$_{1-x}$

Authors: Paul Corbae, Aaron N. Engel, Jason T. Dong, Wilson J. Yánez-Parreño, Donghui Lu, Makoto Hashimoto, Alexei Fedorov, Christopher J. Palmstrøm

Abstract: Bismuth antimony alloys (Bi$_x$Sb$_{1-x}$) provide a tuneable materials platform to study topological transport and spin-polarized surface states resulting from the nontrivial bulk electronic structure. In the two-dimensional limit, it is a suitable system to study the quantum spin Hall effect. In this work we grow epitaxial, single orientation thin films of Bi$_x$Sb$_{1-x}$ on an InSb(111)B subst… ▽ More Bismuth antimony alloys (Bi$_x$Sb$_{1-x}$) provide a tuneable materials platform to study topological transport and spin-polarized surface states resulting from the nontrivial bulk electronic structure. In the two-dimensional limit, it is a suitable system to study the quantum spin Hall effect. In this work we grow epitaxial, single orientation thin films of Bi$_x$Sb$_{1-x}$ on an InSb(111)B substrate down to two bilayers where hybridization effects should gap out the topological surface states. Supported by a tight-binding model, spin- and angle-resolved photoemission spectroscopy data shows pockets at the Fermi level from the topological surface states disappear as the bulk gap increases from confinement. Evidence for a gap opening in the topological surface states is shown in the ultrathin limit. Finally, we observe spin-polarization approaching unity from the topological surface states in 10 bilayer films. The growth and characterization of ultrathin Bi$_x$Sb$_{1-x}$ alloys suggest ultrathin films of this material system can be used to study two-dimensional topological physics as well as applications such as topological devices, low power electronics, and spintronics. △ Less

Submitted 18 September, 2024; originally announced September 2024.

Comments: 7 pages, 4 figures

Role of Coupling Asymmetry in the Fully Disordered Kuramoto Model

Authors: Axel Prüser, Andreas Engel

Abstract: We investigate the dynamics of phase oscillators in the fully disordered Kuramoto model with couplings of defined asymmetry. The mean-field dynamics is reduced to a self-consistent stochastic single-oscillator problem which we analyze perturbatively and by numerical simulations. We elucidate the influence of the asymmetry on the correlation and response function of the system as well as on the dis… ▽ More We investigate the dynamics of phase oscillators in the fully disordered Kuramoto model with couplings of defined asymmetry. The mean-field dynamics is reduced to a self-consistent stochastic single-oscillator problem which we analyze perturbatively and by numerical simulations. We elucidate the influence of the asymmetry on the correlation and response function of the system as well as on the distribution of the order parameter. The so-called volcano transition is shown to be robust with respect to a small degree of coupling asymmetry but to disappear when the antisymmetry in the couplings outweighs the symmetry. △ Less

Submitted 18 December, 2024; v1 submitted 23 August, 2024; originally announced August 2024.

Journal ref: Phys. Rev. E 110, 064214 (2024)

Cryogenic growth of tantalum thin films for low-loss superconducting circuits

Authors: Teun A. J. van Schijndel, Anthony P. McFadden, Aaron N. Engel, Jason T. Dong, Wilson J. Yánez-Parreño, Manisha Parthasarathy, Raymond W. Simmonds, Christopher J. Palmstrøm

Abstract: Motivated by recent advancements highlighting Ta as a promising material in low-loss superconducting circuits and showing long coherence times in superconducting qubits, we have explored the effect of cryogenic temperatures on the growth of Ta and its integration in superconducting circuits. Cryogenic growth of Ta using a low temperature molecular beam epitaxy (MBE) system is found to stabilize si… ▽ More Motivated by recent advancements highlighting Ta as a promising material in low-loss superconducting circuits and showing long coherence times in superconducting qubits, we have explored the effect of cryogenic temperatures on the growth of Ta and its integration in superconducting circuits. Cryogenic growth of Ta using a low temperature molecular beam epitaxy (MBE) system is found to stabilize single phase $α$-Ta on several different substrates, which include Al$\mathrm{_2}$O$\mathrm{_3}$(0001), Si(001), Si(111), SiN${_x}$, and GaAs(001). The substrates are actively cooled down to cryogenic temperatures and remain < 20 K during the Ta deposition. X-ray $θ$-2$θ$ diffraction after warming to room temperature indicates the formation of polycrystalline $α$-Ta. The 50 nm $α$-Ta films grown on Al$\mathrm{_2}$O$\mathrm{_3}$(0001) at a substrate manipulator temperature of 7 K have a room temperature resistivity ($\mathrm{ρ_{300 K}}$) of 13.4 $\mathrm{μΩ}$cm, a residual resistivity ratio (RRR) of 17.3 and a superconducting transition temperature (T$_C$) of 4.14 K, which are comparable to bulk values. In addition, atomic force microscopy (AFM) indicates that the film grown at 7 K with an RMS roughness of 0.45 nm was significantly smoother than the one grown at room temperature. Similar properties are found for films grown on other substrates. Results for films grown at higher substrate manipulator temperatures show higher $\mathrm{ρ_{300 K}}$, lower RRR and Tc, and increased $β$-Ta content. Coplanar waveguide resonators with a gap width of 3 $\mathrmμ$m fabricated from cryogenically grown Ta on Si(111) and Al$\mathrm{_2}$O$\mathrm{_3}$(0001) show low power Q$_i$ of 1.9 million and 0.7 million, respectively, indicating polycrystalline $α$-Ta films may be promising for superconducting qubit applications even though they are not fully epitaxial. △ Less

Submitted 20 May, 2024; originally announced May 2024.

Enhanced mobility of ternary InGaAs quantum wells through digital alloying

Authors: Jason T. Dong, Yilmaz Gul, Aaron N. Engel, Teun A. J. van Schijndel, Connor P. Dempsey, Michael Pepper, Christopher J. Palmstrøm

Abstract: High In content InGaAs quantum wells (In $\geq$ 75%) are potentially useful for topological quantum computing and spintronics applications. In high mobility InGaAs quantum wells, alloy disorder scattering is a limiting factor. In this report, we demonstrate that by growing the InGaAs quantum wells as a digital alloy, or a short period superlattice, we can reduce the alloy disorder scattering withi… ▽ More High In content InGaAs quantum wells (In $\geq$ 75%) are potentially useful for topological quantum computing and spintronics applications. In high mobility InGaAs quantum wells, alloy disorder scattering is a limiting factor. In this report, we demonstrate that by growing the InGaAs quantum wells as a digital alloy, or a short period superlattice, we can reduce the alloy disorder scattering within the quantum well and increase the peak 2 K electron mobility to 545,000 cm^2/V s, which is the highest reported mobility for high In content InGaAs quantum wells to the best of the authors' knowledge. Our results demonstrate that the digital alloy approach can be used to increase the mobility of quantum wells in random alloy ternary materials. △ Less

Submitted 29 March, 2024; v1 submitted 25 March, 2024; originally announced March 2024.

Determining the bulk and surface electronic structure of $α$-Sn/InSb(001) with spin- and angle-resolved photoemission spectroscopy

Authors: Aaron N. Engel, Paul J. Corbae, Hadass S. Inbar, Connor P. Dempsey, Shinichi Nishihaya, Wilson Yánez-Parreño, Yuhao Chang, Jason T. Dong, Alexei V. Fedorov, Makoto Hashimoto, Donghui Lu, Christopher J. Palmstrøm

Abstract: The surface and bulk states in topological materials have shown promise in many applications. Grey or $α$-Sn, the inversion symmetric analogue to HgTe, can exhibit a variety of these phases. However there is disagreement in both calculation and experiment over the exact shape of the bulk bands and the number and origin of the surface states. Using spin- and angle-resolved photoemission we investig… ▽ More The surface and bulk states in topological materials have shown promise in many applications. Grey or $α$-Sn, the inversion symmetric analogue to HgTe, can exhibit a variety of these phases. However there is disagreement in both calculation and experiment over the exact shape of the bulk bands and the number and origin of the surface states. Using spin- and angle-resolved photoemission we investigate the bulk and surface electronic structure of $α$-Sn thin films on InSb(001) grown by molecular beam epitaxy. We find that there is no significant warping in the shapes of the bulk bands. We also observe the presence of only two surface states near the valence band maximum in both thin (13 bilayer) and thick (400 bilayer) films. In 50 bilayer films, these two surface states coexist with quantum well states. Surprisingly, both of these surface states are spin-polarized with orthogonal spin-momentum locking and opposite helicities. One of these states is the spin-polarized topological surface state and the other a spin resonance. Finally, the presence of another orthogonal spin-momentum locked topological surface state from a secondary band inversion is verified. Our work clarifies the electronic structure of $α$-Sn(001) such that better control of the electronic properties can be achieved. In addition, the presence of two spin-polarized surface states near the valence band maximum has important ramifications for the use of $α$-Sn in spintronics. △ Less

Submitted 1 March, 2024; originally announced March 2024.

Strain Solitons in an Epitaxially Strained van der Waals-like Material

Authors: Jason T. Dong, Hadass S. Inbar, Connor P. Dempsey, Aaron N. Engel, Christopher J. Palmstrøm

Abstract: Strain solitons are quasi-dislocations that form in van der Waals materials to relieve the energy associated with lattice or rotational mismatch in the crystal. Novel and unusual electronic properties of strain solitons have been both predicted and observed. To date, strain solitons have only been observed in exfoliated crystals or mechanically strained bulk crystals. The lack of a scalable approa… ▽ More Strain solitons are quasi-dislocations that form in van der Waals materials to relieve the energy associated with lattice or rotational mismatch in the crystal. Novel and unusual electronic properties of strain solitons have been both predicted and observed. To date, strain solitons have only been observed in exfoliated crystals or mechanically strained bulk crystals. The lack of a scalable approach towards the generation of strain solitons poses a significant challenge in the study of and use of the properties of strain solitons. Here we report the formation of strain solitons with epitaxial growth of bismuth on an InSb (111)B substrate by molecular beam epitaxy. The morphology of the strain solitons for films of varying thickness is characterized with scanning tunneling microscopy and the local strain state is determined from the analysis of atomic resolution images. Bending in the solitons is attributed due to interactions with the interface, and large angle bending is associated with edge dislocations. Our results enable the scalable generation of strain solitons. △ Less

Submitted 23 January, 2024; originally announced January 2024.

Growth and characterization of $α$-Sn thin films on In- and Sb-rich reconstructions of InSb(001)

Authors: Aaron N. Engel, Connor P. Dempsey, Hadass S. Inbar, Jason T. Dong, Shinichi Nishihaya, Yu Hao Chang, Alexei V. Fedorov, Makoto Hashimoto, Donghui Lu, Christopher J. Palmstrøm

Abstract: $α$-Sn thin films can exhibit a variety of topologically non-trivial phases. Both studying the transitions between these phases and making use of these phases in eventual applications requires good control over the electronic and structural quality of $α$-Sn thin films. $α$-Sn growth on InSb often results in out-diffusion of indium, a p-type dopant. By growing $α… ▽ More $α$-Sn thin films can exhibit a variety of topologically non-trivial phases. Both studying the transitions between these phases and making use of these phases in eventual applications requires good control over the electronic and structural quality of $α$-Sn thin films. $α$-Sn growth on InSb often results in out-diffusion of indium, a p-type dopant. By growing $α$-Sn via molecular beam epitaxy on the Sb-rich c(4$\times$4) surface reconstruction of InSb(001) rather than the In-rich c(8$\times$2), we demonstrate a route to substantially decrease and minimize this indium incorporation. The reduction in indium concentration allows for the study of the surface and bulk Dirac nodes in $α$-Sn via angle-resolved photoelectron spectroscopy without the common approaches of bulk doping or surface dosing, simplifying topological phase identification. The lack of indium incorporation is verified in angle-resolved and -integrated ultraviolet photoelectron spectroscopy as well as in clear changes in the Hall response. △ Less

Submitted 29 November, 2023; v1 submitted 27 November, 2023; originally announced November 2023.

Nature of the Volcano Transition in the Fully Disordered Kuramoto Model

Authors: Axel Prüser, Sebastian Rosmej, Andreas Engel

Abstract: Randomly coupled phase oscillators may synchronize into disordered patterns of collective motion. We analyze this transition in a large, fully connected Kuramoto model with symmetric but otherwise independent random interactions. Using the dynamical cavity method we reduce the dynamics to a stochastic single-oscillator problem with self-consistent correlation and response functions that we study a… ▽ More Randomly coupled phase oscillators may synchronize into disordered patterns of collective motion. We analyze this transition in a large, fully connected Kuramoto model with symmetric but otherwise independent random interactions. Using the dynamical cavity method we reduce the dynamics to a stochastic single-oscillator problem with self-consistent correlation and response functions that we study analytically and numerically. We clarify the nature of the volcano transition and elucidate its relation to the existence of an oscillator glass phase. △ Less

Submitted 3 May, 2024; v1 submitted 13 October, 2023; originally announced October 2023.

Journal ref: Phys. Rev. Lett. 132, 187201, Published 30 April 2024

Inversion Symmetry Breaking in Epitaxial Ultrathin Bi (111) Films

Authors: Hadass S. Inbar, Muhammad Zubair, Jason T. Dong, Aaron N Engel, Connor P. Dempsey, Yu Hao Chang, Shinichi Nishihaya, Shoaib Khalid, Alexei V. Fedorov, Anderson Janotti, Chris J. Palmstrøm

Abstract: Bismuth (Bi) films hold potential for spintronic devices and topological one-dimensional edge transport. Large-area high-quality (111) Bi ultrathin films are grown on InSb (111)B substrates. Strong film-substrate interactions epitaxially stabilize the (111) orientation and lead to inversion symmetry breaking. We resolve the longstanding controversy over the Z_2 topological assignment of bismuth an… ▽ More Bismuth (Bi) films hold potential for spintronic devices and topological one-dimensional edge transport. Large-area high-quality (111) Bi ultrathin films are grown on InSb (111)B substrates. Strong film-substrate interactions epitaxially stabilize the (111) orientation and lead to inversion symmetry breaking. We resolve the longstanding controversy over the Z_2 topological assignment of bismuth and show that the surface states are topologically trivial. Our results demonstrate that interfacial bonds prevent the semimetal-to-semiconductor transition predicted for freestanding bismuth layers, highlighting the importance of controlled functionalization and surface passivation in two-dimensional materials. △ Less

Submitted 21 April, 2025; v1 submitted 1 February, 2023; originally announced February 2023.

Phonon-induced localization of excitons in molecular crystals from first principles

Authors: Antonios M. Alvertis, Jonah B. Haber, Edgar A. Engel, Sahar Sharifzadeh, Jeffrey B. Neaton

Abstract: The spatial extent of excitons in molecular systems underpins their photophysics and utility for optoelectronic applications. Phonons are reported to lead to both exciton localization and delocalization. However, a microscopic understanding of phonon-induced (de)localization is lacking, in particular how localized states form, the role of specific vibrations, and the relative importance of quantum… ▽ More The spatial extent of excitons in molecular systems underpins their photophysics and utility for optoelectronic applications. Phonons are reported to lead to both exciton localization and delocalization. However, a microscopic understanding of phonon-induced (de)localization is lacking, in particular how localized states form, the role of specific vibrations, and the relative importance of quantum and thermal nuclear fluctuations. Here we present a first-principles study of these phenomena in solid pentacene, a prototypical molecular crystal, capturing the formation of bound excitons, exciton-phonon coupling to all orders, and phonon anharmonicity, using density functional theory, the \emph{ab initio} $GW$-Bethe-Salpeter equation approach, finite difference, and path integral techniques. We find that for pentacene zero-point nuclear motion causes uniformly strong localization, with thermal motion providing additional localization only for Wannier-Mott-like excitons. Anharmonic effects drive temperature-dependent localization, and while such effects prevent the emergence of highly delocalized excitons, we explore the conditions under which these might be realized. △ Less

Submitted 27 January, 2023; originally announced January 2023.

Journal ref: Phys. Rev. Lett. 130, 086401 (2023)

First Principles Assessment of CdTe as a Tunnel Barrier at the $\mathbfα$-Sn/InSb Interface

Authors: Malcolm J. A. Jardine, Derek Dardzinski, Maituo Yu, Amrita Purkayastha, A. -H. Chen, Yu-Hao Chang, Aaron Engel, Vladimir N. Strocov, Moïra Hocevar, Chris J. Palmstrøm, Sergey M. Frolov, Noa Marom

Abstract: Majorana zero modes, with prospective applications in topological quantum computing, are expected to arise in superconductor/semiconductor interfaces, such as $β$-Sn and InSb. However, proximity to the superconductor may also adversely affect the semiconductor's local properties. A tunnel barrier inserted at the interface could resolve this issue. We assess the wide band gap semiconductor, CdTe, a… ▽ More Majorana zero modes, with prospective applications in topological quantum computing, are expected to arise in superconductor/semiconductor interfaces, such as $β$-Sn and InSb. However, proximity to the superconductor may also adversely affect the semiconductor's local properties. A tunnel barrier inserted at the interface could resolve this issue. We assess the wide band gap semiconductor, CdTe, as a candidate material to mediate the coupling at the lattice-matched interface between $α$-Sn and InSb. To this end, we use density functional theory (DFT) with Hubbard U corrections, whose values are machine-learned via Bayesian optimization (BO) [npj Computational Materials 6, 180 (2020)]. The results of DFT+U(BO) are validated against angle resolved photoemission spectroscopy (ARPES) experiments for $α$-Sn and CdTe. For CdTe, the z-unfolding method [Advanced Quantum Technologies, 5, 2100033 (2022)] is used to resolve the contributions of different $k_z$ values to the ARPES. We then study the band offsets and the penetration depth of metal-induced gap states (MIGS) in bilayer interfaces of InSb/$α$-Sn, InSb/CdTe, and CdTe/$α$-Sn, as well as in tri-layer interfaces of InSb/CdTe/$α$-Sn with increasing thickness of CdTe. We find that 16 atomic layers (3.5 nm) of CdTe can serve as a tunnel barrier, effectively shielding the InSb from MIGS from the $α$-Sn. This may guide the choice of dimensions of the CdTe barrier to mediate the coupling in semiconductor-superconductor devices in future Majorana zero modes experiments. △ Less

Submitted 7 January, 2023; originally announced January 2023.

Journal ref: ACS Appl. Mater. Interfaces 2023

Tuning the Band Topology of GdSb by Epitaxial Strain

Authors: Hadass S. Inbar, Dai Q. Ho, Shouvik Chatterjee, Aaron N. Engel, Shoaib Khalid, Connor P. Dempsey, Mihir Pendharkar, Yu Hao Chang, Shinichi Nishihaya, Alexei V. Fedorov, Donghui Lu, Makoto Hashimoto, Dan Read, Anderson Janotti, Christopher J. Palmstrøm

Abstract: Rare-earth monopnictide (RE-V) semimetal crystals subjected to hydrostatic pressure have shown interesting trends in magnetoresistance, magnetic ordering, and superconductivity, with theory predicting pressure-induced band inversion. Yet, thus far, there have been no direct experimental reports of interchanged band order in RE-Vs due to strain. This work studies the evolution of band topology in b… ▽ More Rare-earth monopnictide (RE-V) semimetal crystals subjected to hydrostatic pressure have shown interesting trends in magnetoresistance, magnetic ordering, and superconductivity, with theory predicting pressure-induced band inversion. Yet, thus far, there have been no direct experimental reports of interchanged band order in RE-Vs due to strain. This work studies the evolution of band topology in biaxially strained GdSb (001) epitaxial films using angle-resolved photoemission spectroscopy (ARPES) and density functional theory (DFT). We find that biaxial strain continuously tunes the electronic structure from topologically trivial to nontrivial, reducing the gap between the hole and the electron bands dispersing along the [001] direction. The conduction and valence band shifts seen in DFT and ARPES measurements are explained by a tight-binding model that accounts for the orbital symmetry of each band. Finally, we discuss the effect of biaxial strain on carrier compensation and magnetic ordering temperature. △ Less

Submitted 18 April, 2023; v1 submitted 28 November, 2022; originally announced November 2022.

Topology-dependent coalescence controls scaling exponents in finite networks

Authors: Roxana Zeraati, Victor Buendía, Tatiana A. Engel, Anna Levina

Abstract: Multiple studies of neural avalanches across different data modalities led to the prominent hypothesis that the brain operates near a critical point. The observed exponents often indicate the mean-field directed-percolation universality class, leading to the fully-connected or random network models to study the avalanche dynamics. However, the cortical networks have distinct non-random features an… ▽ More Multiple studies of neural avalanches across different data modalities led to the prominent hypothesis that the brain operates near a critical point. The observed exponents often indicate the mean-field directed-percolation universality class, leading to the fully-connected or random network models to study the avalanche dynamics. However, the cortical networks have distinct non-random features and spatial organization that is known to affect the critical exponents. Here we show that distinct empirical exponents arise in networks with different topology and depend on the network size. In particular, we find apparent scale-free behavior with mean-field exponents appearing as quasi-critical dynamics in structured networks. This quasi-critical dynamics cannot be easily discriminated from an actual critical point in small networks. We find that the local coalescence in activity dynamics can explain the distinct exponents. Therefore, both topology and system size should be considered when assessing criticality from empirical observables. △ Less

Submitted 11 November, 2022; originally announced November 2022.

A data-driven interpretation of the stability of molecular crystals

Authors: Rose K. Cersonsky, Maria Pakhnova, Edgar A. Engel, Michele Ceriotti

Abstract: Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A particularly active and fruitful approach involves classifying the different combinations of interacting chemical moieties, as understanding the relative energetics of di… ▽ More Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A particularly active and fruitful approach involves classifying the different combinations of interacting chemical moieties, as understanding the relative energetics of different interactions enables the design of molecular crystals and fine-tuning their stabilities. While this is usually performed based on the empirical observation of the most commonly encountered motifs in known crystal structures, we propose to apply a combination of supervised and unsupervised machine-learning techniques to automate the construction of an extensive library of molecular building blocks. We introduce a structural descriptor tailored to the prediction of the binding (lattice) energy and apply it to a curated dataset of organic crystals and exploit its atom-centered nature to obtain a data-driven assessment of the contribution of different chemical groups to the lattice energy of the crystal. We then interpret this library using a low-dimensional representation of the structure-energy landscape and discuss selected examples of the insights into crystal engineering that can be extracted from this analysis, providing a complete database to guide the design of molecular materials. △ Less

Submitted 22 December, 2022; v1 submitted 21 September, 2022; originally announced September 2022.

Epitaxial growth, magnetoresistance, and electronic band structure of GdSb magnetic semimetal films

Authors: Hadass S. Inbar, Dai Q. Ho, Shouvik Chatterjee, Mihir Pendharkar, Aaron N. Engel, Jason T. Dong, Shoaib Khalid, Yu Hao Chang, Taozhi Guo, Alexei V. Fedorov, Donghui Lu, Makoto Hashimoto, Dan Read, Anderson Janotti, Christopher J. Palmstrøm

Abstract: Motivated by observations of extreme magnetoresistance (XMR) in bulk crystals of rare-earth monopnictide (RE-V) compounds and emerging applications in novel spintronic and plasmonic devices based on thin-film semimetals, we have investigated the electronic band structure and transport behavior of epitaxial GdSb thin films grown on III-V semiconductor surfaces. The Gd3+ ion in GdSb has a high spin… ▽ More Motivated by observations of extreme magnetoresistance (XMR) in bulk crystals of rare-earth monopnictide (RE-V) compounds and emerging applications in novel spintronic and plasmonic devices based on thin-film semimetals, we have investigated the electronic band structure and transport behavior of epitaxial GdSb thin films grown on III-V semiconductor surfaces. The Gd3+ ion in GdSb has a high spin S=7/2 and no orbital angular momentum, serving as a model system for studying the effects of antiferromagnetic order and strong exchange coupling on the resulting Fermi surface and magnetotransport properties of RE-Vs. We present a surface and structural characterization study mapping the optimal synthesis window of thin epitaxial GdSb films grown on III-V lattice-matched buffer layers via molecular beam epitaxy. To determine the factors limiting XMR in RE-V thin films and provide a benchmark for band structure predictions of topological phases of RE-Vs, the electronic band structure of GdSb thin films is studied, comparing carrier densities extracted from magnetotransport, angle-resolved photoemission spectroscopy (ARPES), and density functional theory (DFT) calculations. ARPES shows hole-carrier rich topologically-trivial semi-metallic band structure close to complete electron-hole compensation, with quantum confinement effects in the thin films observed through the presence of quantum well states. DFT predicted Fermi wavevectors are in excellent agreement with values obtained from quantum oscillations observed in magnetic field-dependent resistivity measurements. An electron-rich Hall coefficient is measured despite the higher hole carrier density, attributed to the higher electron Hall mobility. The carrier mobilities are limited by surface and interface scattering, resulting in lower magnetoresistance than that measured for bulk crystals. △ Less

Submitted 25 October, 2022; v1 submitted 4 August, 2022; originally announced August 2022.

Report number: Phys. Rev. Materials 6, L121201

Journal ref: Phys. Rev. Materials 6, L121201 (2022)

Spatial and temporal correlations in neural networks with structured connectivity

Authors: Yan-Liang Shi, Roxana Zeraati, Anna Levina, Tatiana A. Engel

Abstract: Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed correlations in either spatial or temporal domains, oblivious to their interplay. We show that the network dynamics and connectivity jointly define the spatiotemp… ▽ More Correlated fluctuations in the activity of neural populations reflect the network's dynamics and connectivity. The temporal and spatial dimensions of neural correlations are interdependent. However, prior theoretical work mainly analyzed correlations in either spatial or temporal domains, oblivious to their interplay. We show that the network dynamics and connectivity jointly define the spatiotemporal profile of neural correlations. We derive analytical expressions for pairwise correlations in networks of binary units with spatially arranged connectivity in one and two dimensions. We find that spatial interactions among units generate multiple timescales in auto- and cross-correlations. Each timescale is associated with fluctuations at a particular spatial frequency, making a hierarchical contribution to the correlations. External inputs can modulate the correlation timescales when spatial interactions are nonlinear, and the modulation effect depends on the operating regime of network dynamics. These theoretical results open new ways to relate connectivity and dynamics in cortical networks via measurements of spatiotemporal neural correlations. △ Less

Submitted 16 July, 2022; originally announced July 2022.

Comments: 25 pages, 20 figures

Stiffness of random walks with reflecting boundary conditions

Authors: Sascha Kaldasch, Andreas Engel

Abstract: We study the distribution of occupation times for a one-dimensional random walk restricted to a finite interval by reflecting boundary conditions. At short times the classical bimodal distribution due to Lévy is reproduced with walkers staying mostly either left or right to the initial point. With increasing time, however, the boundaries suppress large excursions from the starting point, and the d… ▽ More We study the distribution of occupation times for a one-dimensional random walk restricted to a finite interval by reflecting boundary conditions. At short times the classical bimodal distribution due to Lévy is reproduced with walkers staying mostly either left or right to the initial point. With increasing time, however, the boundaries suppress large excursions from the starting point, and the distribution becomes unimodal converging to a $δ$-distribution in the long time limit. An approximate spectral analysis of the underlying Fokker-Planck equation yields results in excellent agreement with numerical simulations. △ Less

Submitted 15 October, 2021; v1 submitted 29 September, 2021; originally announced September 2021.

Comments: 6 pages, 9 figures, references added, small adjustments in the text

The importance of nuclear quantum effects for NMR crystallography

Authors: Edgar A. Engel, Venkat Kapil, Michele Ceriotti

Abstract: The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of computational predictions of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy. To test the limits of this approximation, we systematically study the importance of finite-temperature and quantum nuclear fluctuations… ▽ More The resolving power of solid-state nuclear magnetic resonance (NMR) crystallography depends heavily on the accuracy of computational predictions of NMR chemical shieldings of candidate structures, which are usually taken to be local minima in the potential energy. To test the limits of this approximation, we systematically study the importance of finite-temperature and quantum nuclear fluctuations for $^1$H, $^{13}$C, and $^{15}$N shieldings in polymorphs of three paradigmatic molecular crystals -- benzene, glycine, and succinic acid. The effect of quantum fluctuations is comparable to the typical errors of shielding predictions for static nuclei with respect to experiments, and their inclusion to improve the agreement with measurements, translating to more reliable assignment of the NMR spectra to the correct candidate structure. The use of integrated machine-learning models, trained on first-principles energies and shieldings, renders rigorous sampling of nuclear fluctuations affordable, setting a new standard for the calculations underlying NMR structure determinations. △ Less

Submitted 9 January, 2022; v1 submitted 27 June, 2021; originally announced June 2021.

Journal ref: J. Phys. Chem. Lett. 12(32), 7701-7707 (2021)

Aspects of a phase transition in high-dimensional random geometry

Authors: Axel Prüser, Imre Kondor, Andreas Engel

Abstract: A phase transition in high-dimensional random geometry is analyzed as it arises in a variety of problems. A prominent example is the feasibility of a minimax problem that represents the extremal case of a class of financial risk measures, among them the current regulatory market risk measure Expected Shortfall. Others include portfolio optimization with a ban on short selling, the storage capacity… ▽ More A phase transition in high-dimensional random geometry is analyzed as it arises in a variety of problems. A prominent example is the feasibility of a minimax problem that represents the extremal case of a class of financial risk measures, among them the current regulatory market risk measure Expected Shortfall. Others include portfolio optimization with a ban on short selling, the storage capacity of the perceptron, the solvability of a set of linear equations with random coefficients, and competition for resources in an ecological system. These examples shed light on various aspects of the underlying geometric phase transition, create links between problems belonging to seemingly distant fields and offer the possibility for further ramifications. △ Less

Submitted 17 June, 2021; v1 submitted 10 May, 2021; originally announced May 2021.

Journal ref: Entropy 2021, 23(7), 805

A complete description of thermodynamic stabilities of molecular crystals

Authors: Venkat Kapil, Edgar A Engel

Abstract: Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free energy differences are sensitively affected by the description of electronic structure, the statistical mechanics of the nuclei and the cell, and thermal expans… ▽ More Predictions of relative stabilities of (competing) molecular crystals are of great technological relevance, most notably for the pharmaceutical industry. However, they present a long-standing challenge for modeling, as often minuscule free energy differences are sensitively affected by the description of electronic structure, the statistical mechanics of the nuclei and the cell, and thermal expansion. The importance of these effects has been individually established, but rigorous free energy calculations for general molecular compounds, which simultaneously account for all effects,have hitherto not been computationally viable. Here we present an efficient "end to end" frame-work that seamlessly combines state-of-the art electronic structure calculations, machine-learning potentials, and advanced free energy methods to calculate ab initio Gibbs free energies for general organic molecular materials. The facile generation of machine-learning potentials for a diverse set of polymorphic compounds, benzene, glycine, and succinic acid, and predictions of thermodynamic stabilities in qualitative and quantitative agreement with experiments highlights that predictive thermodynamic studies of industrially-relevant molecular materials are no longer a daunting task. △ Less

Submitted 27 January, 2022; v1 submitted 26 February, 2021; originally announced February 2021.

Learning non-stationary Langevin dynamics from stochastic observations of latent trajectories

Authors: Mikhail Genkin, Owen Hughes, Tatiana A. Engel

Abstract: Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their function. However, dynamics are often inaccessible directly and can be only gleaned through a stochastic observation process, which makes the inference challengin… ▽ More Many complex systems operating far from the equilibrium exhibit stochastic dynamics that can be described by a Langevin equation. Inferring Langevin equations from data can reveal how transient dynamics of such systems give rise to their function. However, dynamics are often inaccessible directly and can be only gleaned through a stochastic observation process, which makes the inference challenging. Here we present a non-parametric framework for inferring the Langevin equation, which explicitly models the stochastic observation process and non-stationary latent dynamics. The framework accounts for the non-equilibrium initial and final states of the observed system and for the possibility that the system's dynamics define the duration of observations. Omitting any of these non-stationary components results in incorrect inference, in which erroneous features arise in the dynamics due to non-stationary data distribution. We illustrate the framework using models of neural dynamics underlying decision making in the brain. △ Less

Submitted 29 December, 2020; originally announced December 2020.

Journal ref: Nat Commun 12, 5986 (2021)

Stiffness of Probability Distributions of Work and Jarzynski Relation for Initial Microcanonical and Energy Eigenstates

Authors: Lars Knipschild, Andreas Engel, Jochen Gemmer

Abstract: We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. As a starting point we assume that, for systems initialized in microcanonical states at some energies, the resulting probability densities of work (work-PDFs) are largely independent of these specific initial energies. We show analytically that this assumption of "… ▽ More We consider closed quantum systems (into which baths may be integrated) that are driven, i.e., subject to time-dependent Hamiltonians. As a starting point we assume that, for systems initialized in microcanonical states at some energies, the resulting probability densities of work (work-PDFs) are largely independent of these specific initial energies. We show analytically that this assumption of "stiffness", together with the assumption of an exponentially growing density of energy eigenstates, is sufficient but not necessary for the validity of the Jarzynski relation (JR) for the above microcanonical initial states. This holds, even in the absence of microreversibility. To scrutinize the connection between stiffness and the JR for microcanonical initial states, we perform numerical analysis on systems comprising random matrices which may be tuned from stiff to nonstiff. In these examples we find the JR fulfilled in the presence of stiffness, and violated in its absence, which indicates a very close connection between stiffness and the JR. Remarkably, in the limit of large systems, we find the JR fulfilled, even for pure initial energy eigenstates. As this has no analogue in classical systems, we consider it a genuine quantum phenomenon. △ Less

Submitted 23 July, 2020; originally announced July 2020.

Comments: 9 pages, 6 figures

Journal ref: Phys. Rev. E 103, 062139 (2021)

Extracting ice phases from liquid water: why a machine-learning water model generalizes so well

Authors: Bartomeu Monserrat, Jan Gerit Brandenburg, Edgar A. Engel, Bingqing Cheng

Abstract: We investigate the structural similarities between liquid water and 53 ices, including 20 knowncrystalline phases. We base such similarity comparison on the local environments that consist of atoms within a certain cutoff radius of a central atom. We reveal that liquid water explores the localenvironments of the diverse ice phases, by directly comparing the environments in these phases using gener… ▽ More We investigate the structural similarities between liquid water and 53 ices, including 20 knowncrystalline phases. We base such similarity comparison on the local environments that consist of atoms within a certain cutoff radius of a central atom. We reveal that liquid water explores the localenvironments of the diverse ice phases, by directly comparing the environments in these phases using general atomic descriptors, and also by demonstrating that a machine-learning potential trained on liquid water alone can predict the densities, the lattice energies, and vibrational properties of theices. The finding that the local environments characterising the different ice phases are found in water sheds light on water phase behaviors, and rationalizes the transferability of water models between different phases. △ Less

Submitted 23 June, 2020; originally announced June 2020.

Work statistics in the periodically driven quartic oscillator: classical versus quantum dynamics

Authors: Mattes Heerwagen, Andreas Engel

Abstract: In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external force with slowly varying amplitude both classically and within the framework of quantum mechanics. The energy change of the oscillator induced by the driving is c… ▽ More In the thermodynamics of nanoscopic systems the relation between classical and quantum mechanical description is of particular importance. To scrutinize this correspondence we study an anharmonic oscillator driven by a periodic external force with slowly varying amplitude both classically and within the framework of quantum mechanics. The energy change of the oscillator induced by the driving is closely related to the probability distribution of work for the system. With the amplitude $λ(t)$ of the drive increasing from zero to a maximum $λ_{max}$ and then going back to zero again initial and final Hamiltonian coincide. The main quantity of interest is then the probability density $P(E_f|E_i)$ for transitions from initial energy $E_i$ to final energy $E_f$. In the classical case non-diagonal transitions with $E_f\neq E_i$ mainly arise due to the mechanism of separatrix crossing. We show that approximate analytical results within the pendulum approximation are in accordance with numerical simulations. In the quantum case numerically exact results are complemented with analytical arguments employing Floquet theory. For both classical and quantum case we provide an intuitive explanation for the periodic variation of $P(E_f|E_i)$ with the maximal amplitude $λ_{max}$ of the driving. △ Less

Submitted 25 August, 2020; v1 submitted 22 April, 2020; originally announced April 2020.

Comments: 12 pages, 11 figures

Journal ref: Phys. Rev. E 102, 022121 (2020)

Large systems of random linear equations with non-negative solutions: Characterizing the solvable and unsolvable phase

Authors: Stefan Landmann, Andreas Engel

Abstract: Large systems of linear equations are ubiquitous in science. Quite often, e.g. when considering population dynamics or chemical networks, the solutions must be non-negative. Recently, it has been shown that large systems of random linear equations exhibit a sharp transition from a phase, where a non-negative solution exists with probability one, to one where typically no such solution may be found… ▽ More Large systems of linear equations are ubiquitous in science. Quite often, e.g. when considering population dynamics or chemical networks, the solutions must be non-negative. Recently, it has been shown that large systems of random linear equations exhibit a sharp transition from a phase, where a non-negative solution exists with probability one, to one where typically no such solution may be found. The critical line separating the two phases was determined by combining Farkas' lemma with the replica method. Here, we show that the same methods remain viable to characterize the two phases away from criticality. To this end we analytically determine the residual norm of the system in the unsolvable phase and a suitable measure of robustness of solutions in the solvable one. Our results are in very good agreement with numerical simulations. △ Less

Submitted 28 February, 2020; originally announced February 2020.

Comments: 9 pages, 9 figures

Journal ref: Phys. Rev. E 101, 062119 (2020)

On non-negative solutions to large systems of random linear equations

Authors: Stefan Landmann, Andreas Engel

Abstract: Systems of random linear equations may or may not have solutions with all components being non-negative. The question is, e.g., of relevance when the unknowns are concentrations or population sizes. In the present paper we show that if such systems are large the transition between these two possibilities occurs at a sharp value of the ratio between the number of unknowns and the number of equation… ▽ More Systems of random linear equations may or may not have solutions with all components being non-negative. The question is, e.g., of relevance when the unknowns are concentrations or population sizes. In the present paper we show that if such systems are large the transition between these two possibilities occurs at a sharp value of the ratio between the number of unknowns and the number of equations. We analytically determine this threshold as a function of the statistical properties of the random parameters and show its agreement with numerical simulations. We also make contact with two special cases that have been studied before: the storage problem of a perceptron and the resource competition model of MacArthur. △ Less

Submitted 15 April, 2019; originally announced April 2019.

Comments: 10 pages, 5 figures

Ab initio thermodynamics of liquid and solid water

Authors: Bingqing Cheng, Edgar A. Engel, Jörg Behler, Christoph Dellago, Michele Ceriotti

Abstract: Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations and proton disorder. This is made possible by combining advanced free energy methods and state-of-the-art machine learning techniques. The ab initio descr… ▽ More Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations and proton disorder. This is made possible by combining advanced free energy methods and state-of-the-art machine learning techniques. The ab initio description leads to structural properties in excellent agreement with experiments, and reliable estimates of the melting points of light and heavy water. We observe that nuclear quantum effects contribute a crucial 0.2 meV/H$_2$O to the stability of ice Ih, making it more stable than ice Ic. Our computational approach is general and transferable, providing a comprehensive framework for quantitative predictions of ab initio thermodynamic properties using machine learning potentials as an intermediate step. △ Less

Submitted 21 November, 2018; originally announced November 2018.

Journal ref: PNAS 116(4), 1110-1115 (2019)

Systems of random linear equations and the phase transition in MacArthur's resource-competition model

Authors: Stefan Landmann, Andreas Engel

Abstract: Complex ecosystems generally consist of a large number of different species utilizing a large number of different resources. Several of their features cannot be captured by models comprising just a few species and resources. Recently, Tikhonov and Monasson have shown that a high-dimensional version of MacArthur's resource competition model exhibits a phase transition from a 'vulnerable' to a 'shie… ▽ More Complex ecosystems generally consist of a large number of different species utilizing a large number of different resources. Several of their features cannot be captured by models comprising just a few species and resources. Recently, Tikhonov and Monasson have shown that a high-dimensional version of MacArthur's resource competition model exhibits a phase transition from a 'vulnerable' to a 'shielded' phase in which the species collectively protect themselves against an inhomogeneous resource influx from the outside. Here we point out that this transition is more general and may be traced back to the existence of non-negative solutions to large systems of random linear equations. Employing Farkas' Lemma we map this problem to the properties of a fractional volume in high dimensions which we determine using methods from the statistical mechanics of disordered systems. △ Less

Submitted 15 October, 2018; v1 submitted 29 June, 2018; originally announced June 2018.

Comments: Updated version accepted for publication in Europhysics Letters. New titel, additional References and expanded supplementary material. 5 pages, 3 figures

Journal ref: Europhysics Letters 124 18004 (2018)

Generalized convex hull construction for materials discovery

Authors: Andrea Anelli, Edgar A. Engel, Chris J. Pickard, Michele Ceriotti

Abstract: High-throughput computational materials searches generate large databases of locally-stable structures. Conventionally, the needle-in-a-haystack search for the few experimentally-synthesizable compounds is performed using a convex hull construction, which identifies structures stabilized by manipulation of a particular thermodynamic constraint (for example pressure or composition) chosen based on… ▽ More High-throughput computational materials searches generate large databases of locally-stable structures. Conventionally, the needle-in-a-haystack search for the few experimentally-synthesizable compounds is performed using a convex hull construction, which identifies structures stabilized by manipulation of a particular thermodynamic constraint (for example pressure or composition) chosen based on prior experimental evidence or intuition. To address the biased nature of this procedure we introduce a generalized convex hull framework. Convex hulls are constructed on data-driven principal coordinates, which represent the full structural diversity of the database. Their coupling to experimentally-realizable constraints hints at the conditions that are most likely to stabilize a given configuration. The probabilistic nature of our framework also addresses the uncertainty stemming from the use of approximate models during database construction, and eliminates redundant structures. The remaining small set of candidates that have a high probability of being synthesizable provide a much needed starting point for the determination of viable synthetic pathways. △ Less

Submitted 9 October, 2018; v1 submitted 5 March, 2018; originally announced March 2018.

Comments: Accepted Manuscript

Journal ref: Phys. Rev. Materials 2, 103804 (2018)

Stochastic thermodynamics of interacting degrees of freedom: Fluctuation theorems for detached path probabilities

Authors: Jannik Ehrich, Andreas Engel

Abstract: Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a series of special cases including measurement-feedback systems, sensors and hidden Markov models. For these special cases we show that fluctuation theorems invol… ▽ More Systems with interacting degrees of freedom play a prominent role in stochastic thermodynamics. Our aim is to use the concept of detached path probabilities and detached entropy production for bipartite Markov processes and elaborate on a series of special cases including measurement-feedback systems, sensors and hidden Markov models. For these special cases we show that fluctuation theorems involving the detached entropy production recover known results which have been obtained separately before. Additionally, we show that the fluctuation relation for the detached entropy production can be used in model selection for data stemming from a hidden Markov model. We discuss the relation to previous approaches including those which use information flow or learning rate to quantify the influence of one subsystem on the other. In conclusion, we present a complete framework with which to find fluctuation relations for coupled systems. △ Less

Submitted 16 October, 2017; v1 submitted 24 July, 2017; originally announced July 2017.

Comments: 10 pages, 7 figures

Journal ref: Phys. Rev. E 96, 042129 (2017)

Design of NbN superconducting nanowire single photon detectors with enhanced infrared photon detection efficiency

Authors: Qiang Wang, Jelmer J. Renema, Andreas Engel, Michiel J. A. de Dood

Abstract: We propose an optimized design for nanowire superconducting single photon detectors, using the recently discovered position dependent detection efficiency in these devices. This knowledge allows an optimized the design of meandering wire NbN detectors by altering the field distribution across the wire. In order to calculate the response of the detectors with different geometries, we use a monotoni… ▽ More We propose an optimized design for nanowire superconducting single photon detectors, using the recently discovered position dependent detection efficiency in these devices. This knowledge allows an optimized the design of meandering wire NbN detectors by altering the field distribution across the wire. In order to calculate the response of the detectors with different geometries, we use a monotonic local detection efficiency from a nanowire and optical absorption distribution via finite-different-time-domain simulations. The calculations predict a trade-off between average absorption and the edge effect leading to a predicted optimal wire width close to 100 nm for 1550 nm wavelength, which drops to 50 nm wire width for 600 nm wavelength. The absorption at the edges can be enhanced by depositing a silicon nanowire on top of the superconducting nanowire, which improves both the total absorption efficiency as well as the internal detection efficiency of meandering wire structures. △ Less

Submitted 14 June, 2017; v1 submitted 8 December, 2016; originally announced December 2016.

Comments: 10 pages, 5 figures

Large deviations in Taylor dispersion

Authors: Marcel Kahlen, Andreas Engel, Christian Van den Broeck

Abstract: We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of the long-time regime for Taylor dispersion. We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of the long-time regime for Taylor dispersion. △ Less

Submitted 24 November, 2016; originally announced November 2016.

Comments: accepted for PRE, 8 pages, 10 figures

Characteristics of superconducting tungsten silicide WxSi1-x for single photon detection

Authors: X. Zhang, A. Engel, Q. Wang, A. Schilling, A. Semenov, M. Sidorova, H. -W. Hübers, I. Charaev, K. Ilin, M. Siegel

Abstract: Superconducting properties of three series of amorphous WxSi1-x films with different thickness and stoichiometry were investigated by dc transport measurements in a magnetic field up to 9 T. These amorphous WxSi1-x films were deposited by magnetron co-sputtering of the elemental source targets onto silicon substrates at room temperature and patterned in form of bridges by optical lithography and r… ▽ More Superconducting properties of three series of amorphous WxSi1-x films with different thickness and stoichiometry were investigated by dc transport measurements in a magnetic field up to 9 T. These amorphous WxSi1-x films were deposited by magnetron co-sputtering of the elemental source targets onto silicon substrates at room temperature and patterned in form of bridges by optical lithography and reactive ion etching. Analysis of the data on magnetoconductivity allowed us to extract the critical temperature, superconducting coherence length, magnetic penetration depth, and diffusion coefficient of electrons in the normal state as a function of film thickness for each stoichiometry. Two basic time constants were derived from transport and time-resolving measurements. A dynamic process of the formation of a hot-spot was analyzed in the framework of a diffusion-based vortex-entry model. We used the two stage diffusion approach and defined a hotspot size by assuming that the quasi-particles and normal-state electrons have the equal diffusion constant. Our findings are consistent with the most recent results on a hot-spot relaxation time in the WxSi1-x superconducting nanowire single-photon detector. In the 5 nm thick W0.85Si0.15 film the hot-spot has a diameter of 105 nm at the peak of the number of non-equilibrium quasi-particles. △ Less

Submitted 14 November, 2016; v1 submitted 26 July, 2016; originally announced July 2016.

Journal ref: Phys. Rev. B 94, 174509 (2016)

Vibrational renormalisation of the electronic band gap in hexagonal and cubic ice

Authors: Edgar A. Engel, Bartomeu Monserrat, Richard J. Needs

Abstract: Electron-phonon coupling in hexagonal and cubic water ice is studied using first-principles quantum mechanical methods. We consider 29 distinct hexagonal and cubic ice proton-orderings with up to 192 molecules in the simulation cell to account for proton-disorder. We find quantum zero-point vibrational corrections to the minimum electronic band gaps ranging from -1.5 to -1.7 eV, which leads to imp… ▽ More Electron-phonon coupling in hexagonal and cubic water ice is studied using first-principles quantum mechanical methods. We consider 29 distinct hexagonal and cubic ice proton-orderings with up to 192 molecules in the simulation cell to account for proton-disorder. We find quantum zero-point vibrational corrections to the minimum electronic band gaps ranging from -1.5 to -1.7 eV, which leads to improved agreement between calculated and experimental band gaps. Anharmonic nuclear vibrations play a negligible role in determining the gaps. Deuterated ice has a smaller band-gap correction at zero-temperature of -1.2 to -1.4eV. Vibrations reduce the differences between the electronic band gaps of different proton-orderings from around 0.17 eV to less than 0.05 eV, so that the electronic band gaps of hexagonal and cubic ice are almost independent of the proton-ordering when quantum nuclear vibrations are taken into account. The comparatively small reduction in the band gap over the temperature range 0-240 K of around 0.1 eV does not depend on the proton ordering, or whether the ice is protiated or deuterated, or hexagonal or cubic. We explain this in terms of the atomistic origin of the strong electron-phonon coupling in ice. △ Less

Submitted 20 May, 2016; originally announced May 2016.

Comments: 10 pages, 9 figures

Journal ref: Journal of Chemical Physics, 143, 244708 (2015)

Level 2 large deviation functionals for systems with and without detailed balance

Authors: Johannes Hoppenau, Daniel Nickelsen, Andreas Engel

Abstract: Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 large deviation {\em functional} characterizing the empirical density of the underlying stochastic process. For Langevin systems obeying detailed balance, the explicit form of this functional has been known ever since the mathematical work of Donsker… ▽ More Large deviation functions are an essential tool in the statistics of rare events. Often they can be obtained by contraction from a so-called level 2 large deviation {\em functional} characterizing the empirical density of the underlying stochastic process. For Langevin systems obeying detailed balance, the explicit form of this functional has been known ever since the mathematical work of Donsker and Varadhan. We rederive the Donsker-Varadhan result by using stochastic path-integrals and then generalize it to situations without detailed balance including non-equilibrium steady states. The proper incorporation of the empirical probability flux turns out to be crucial. We elucidate the relation between the large deviation functional and different notions of entropy production in stochastic thermodynamics and discuss some aspects of the ensuing contractions. Finally, we illustrate our findings with examples. △ Less

Submitted 8 February, 2016; originally announced February 2016.

Comments: 25 pages, 10 figures

Giant electron-phonon interactions in molecular crystals and the importance of non-quadratic coupling

Authors: Bartomeu Monserrat, Edgar A. Engel, Richard J. Needs

Abstract: We investigate electron-phonon coupling in the molecular crystals CH$_4$, NH$_3$, H$_2$O, and HF, using first-principles quantum mechanical calculations. We find vibrational corrections to the electronic band gaps at zero temperature of -1.97 eV, -1.01 eV, -1.52 eV, and -1.62 eV, respectively, which are comparable in magnitude to those from electron-electron correlation effects. Microscopically, t… ▽ More We investigate electron-phonon coupling in the molecular crystals CH$_4$, NH$_3$, H$_2$O, and HF, using first-principles quantum mechanical calculations. We find vibrational corrections to the electronic band gaps at zero temperature of -1.97 eV, -1.01 eV, -1.52 eV, and -1.62 eV, respectively, which are comparable in magnitude to those from electron-electron correlation effects. Microscopically, the strong electron-phonon coupling arises in roughly equal measure from the almost dispersionless high-frequency molecular modes and from the lower frequency lattice modes. We also highlight the limitations of the widely used Allen-Heine-Cardona theory, which gives significant discrepancies compared to our more accurate treatment. △ Less

Submitted 27 October, 2015; originally announced October 2015.

Comments: 6 pages, 4 figures

Journal ref: Phys. Rev. B 92, 140302(R) (2015)

Anharmonic nuclear motion and the relative stability of hexagonal and cubic ice

Authors: Edgar A. Engel, Bartomeu Monserrat, Richard J. Needs

Abstract: We use extensive first-principles quantum mechanical calculations to show that, although the static lattice and harmonic vibrational energies are almost identical, the anharmonic vibrational energy of hexagonal ice is significantly lower than that of cubic ice. This difference in anharmonicity is crucial, stabilising hexagonal ice compared with cubic ice by at least 1.4 meV/H2O, in agreement with… ▽ More We use extensive first-principles quantum mechanical calculations to show that, although the static lattice and harmonic vibrational energies are almost identical, the anharmonic vibrational energy of hexagonal ice is significantly lower than that of cubic ice. This difference in anharmonicity is crucial, stabilising hexagonal ice compared with cubic ice by at least 1.4 meV/H2O, in agreement with experimental estimates. The difference in anharmonicity arises predominantly from molecular O-H bond stretching vibrational modes and is related to the different stacking of atomic layers. △ Less

Submitted 12 August, 2015; originally announced August 2015.

Journal ref: Physical Review X 5, 021033 (2015)

Superconductivity in the ferromagnetic semiconductor SmN

Authors: E. -M. Anton, S. Granville, A. Engel, S. V. Chong, M. Governale, U. Zülicke, A. G. Moghaddam, H. J. Trodahl, F. Natali, S. Vézian, B. J. Ruck

Abstract: The discovery of materials that simultaneously host different phases of matter has often initially confounded, but ultimately enhanced, our basic understanding of the coexisting types of order. The associated intellectual challenges, together with the promise of greater versatility for potential applications, have made such systems a focus of modern materials science. In particular, great efforts… ▽ More The discovery of materials that simultaneously host different phases of matter has often initially confounded, but ultimately enhanced, our basic understanding of the coexisting types of order. The associated intellectual challenges, together with the promise of greater versatility for potential applications, have made such systems a focus of modern materials science. In particular, great efforts have recently been devoted to making semiconductors ferromagnetic and metallic ferromagnets superconducting. Here we report the unprecedented observation of a heavily donor-doped ferromagnetic semiconductor, SmN, becoming superconducting with ferromagnetism remaining intact. The extremely large exchange splitting of the conduction and valence bands in this material necessitates that the superconducting order hosted by SmN is of an unconventional triplet type, most likely exhibiting p-wave symmetry. Short range spin fluctuations, which are thought to be the cause of pairing interactions in currently known triplet superconductors, are quenched in SmN, suggesting its superconductivity to be the result of phonon- or Coulomb-mediated pairing mechanisms. This scenario is further supported by the inferred heavy mass of superconducting charge carriers. The unique near-zero magnetisation associated with the ferromagnetic state in SmN further aids its coexistence with superconductivity. Presenting this novel material system where semiconducting, ferromagnetic and superconducting properties are combined provides a versatile new laboratory for studying quantum phases of matter. Moreover it is a major step towards identifying materials that merge superconductivity and spintronics, urgently needed to enable the design of electronic devices with superior functionality. △ Less

Submitted 2 March, 2016; v1 submitted 14 May, 2015; originally announced May 2015.

Comments: 8 pages, 5 figures, main text plus supplemental material

Journal ref: Phys. Rev. B 94, 024106 (2016)

Position-Dependent Local Detection Efficiency in a Nanowire Superconducting Single-Photon Detector

Authors: Jelmer J. Renema, Qiang Wang, Rosalinda Gaudio, Irina Komen, Koen op 't Hoog, Dondu Sahin, Andreas Schilling, Martin P. van Exter, Andrea Fiore, Andreas Engel, Michiel J. A. de Dood

Abstract: We probe the local detection efficiency in a nanowire superconducting single-photon detector along the cross-section of the wire with a spatial resolution of 10 nm. We experimentally find a strong variation in the local detection efficiency of the device. We demonstrate that this effect explains previously observed variations in NbN detector efficiency as function of device geometry. We probe the local detection efficiency in a nanowire superconducting single-photon detector along the cross-section of the wire with a spatial resolution of 10 nm. We experimentally find a strong variation in the local detection efficiency of the device. We demonstrate that this effect explains previously observed variations in NbN detector efficiency as function of device geometry. △ Less

Submitted 20 April, 2015; originally announced April 2015.

Stochastic thermodynamics of rapidly driven systems

Authors: Gregory Bulnes Cuetara, Andreas Engel, Massimiliano Esposito

Abstract: We present the stochastic thermodynamics analysis of an open quantum system weakly coupled to multiple reservoirs and driven by a rapidly oscillating external field. The analysis is built on a modified stochastic master equation in the Floquet basis. Transition rates are shown to satisfy the local detailed balance involving the entropy flowing out of the reservoirs. The first and second law of the… ▽ More We present the stochastic thermodynamics analysis of an open quantum system weakly coupled to multiple reservoirs and driven by a rapidly oscillating external field. The analysis is built on a modified stochastic master equation in the Floquet basis. Transition rates are shown to satisfy the local detailed balance involving the entropy flowing out of the reservoirs. The first and second law of thermodynamics are also identified at the trajectory level. Mechanical work is identified by means of initial and final projections on energy eigenstates of the system. We explicitly show that this two step measurement becomes unnecessary in the long time limit. A steady-state fluctuation theorem for the currents and rate of mechanical work is also established. This relation does not require the introduction of a time reversed external driving which is usually needed when considering systems subjected to time asymmetric external fields. This is understood as a consequence of the secular approximation applied in consistency with the large time scale separation between the fast driving oscillations and the slower relaxation dynamics induced by the environment. Our results are finally illustrated on a model describing a thermodynamic engine. △ Less

Submitted 11 May, 2015; v1 submitted 30 November, 2014; originally announced December 2014.

Comments: Equation (31) removed and subsequent discussion improved. References improved and minor corrections. v3: published version

Journal ref: New J. Phys. 17 055002 (2015)

Detection Mechanism in SNSPD: Numerical Results of a Conceptually Simple, Yet Powerful Detection Model

Authors: Andreas Engel, Julia Lonsky, Xiaofu Zhang, Andreas Schilling

Abstract: In a recent publication we have proposed a numerical model that describes the detection process of optical photons in superconducting nanowire single-photon detectors (SNSPD). Here, we review this model and present a significant improvement that allows us to calculate more accurate current distributions for the inhomogeneous quasi-particle densities occurring after photon absorption. With this new… ▽ More In a recent publication we have proposed a numerical model that describes the detection process of optical photons in superconducting nanowire single-photon detectors (SNSPD). Here, we review this model and present a significant improvement that allows us to calculate more accurate current distributions for the inhomogeneous quasi-particle densities occurring after photon absorption. With this new algorithm we explore the detector response in standard NbN SNSPD for photons absorbed off-center and for 2-photon processes. We also discuss the outstanding performance of SNSPD based on WSi. Our numerical results indicate a different detection mechanism in WSi than in NbN or similar materials. △ Less

Submitted 21 August, 2014; originally announced August 2014.

Comments: Presented at ASC 2014 (invited) and submitted to IEEE Transaction on Applied Superconductivity (Special Issue)

Journal ref: Applied Superconductivity, IEEE Transactions on (Volume:25 , Issue: 3 ) 2200407, 2015

On the energetics of information exchange

Authors: Johannes Hoppenau, Andreas Engel

Abstract: We consider the thermodynamic properties of systems in contact with an information source and focus on the consequences of energetic cost associated with the exchange of information. To this end we introduce the model of a thermal tape and derive a general bound for the efficiency of work extraction for systems in contact with such a tape. Depending on the perspective, the correlations between sys… ▽ More We consider the thermodynamic properties of systems in contact with an information source and focus on the consequences of energetic cost associated with the exchange of information. To this end we introduce the model of a thermal tape and derive a general bound for the efficiency of work extraction for systems in contact with such a tape. Depending on the perspective, the correlations between system and tape may either increase or reduce the efficiency of the device. We illustrate our general results with two exactly solvable models, one being an autonomous system, the other one involving measurement and feedback. We also define an ideal tape limit in which our findings reduce to known results. △ Less

Submitted 10 January, 2014; originally announced January 2014.

Comments: 6 pages, 6 figures

Numerical analysis of detection-mechanism models of SNSPD

Authors: Andreas Engel, Andreas Schilling

Abstract: The microscopic mechanism of photon detection in superconducting nanowire single-photon detectors is still under debate. We present a simple, but powerful theoretical model that allows us to identify essential differences between competing detection mechanisms. The model is based on quasi-particle multiplication and diffusion after the absorption of a photon. We then use the calculated spatial and… ▽ More The microscopic mechanism of photon detection in superconducting nanowire single-photon detectors is still under debate. We present a simple, but powerful theoretical model that allows us to identify essential differences between competing detection mechanisms. The model is based on quasi-particle multiplication and diffusion after the absorption of a photon. We then use the calculated spatial and temporal evolution of this quasi-particle cloud to determine detection criteria of three distinct detection mechanisms, based on the formation of a normal conducting spot, the reduction of the effective depairing critical current below the bias current and a vortex-crossing scenario, respectively. All our calculations as well as a comparison to experimental data strongly support the vortex-crossing detection mechanism by which vortices and antivortices enter the superconducting strip from the edges and subsequently traverse it thereby triggering the detectable normal conducting domain. These results may therefore help to reveal the microscopic mechanism responsible for the detection of photons in superconducting nanowires. △ Less

Submitted 12 November, 2013; v1 submitted 27 August, 2013; originally announced August 2013.

Comments: 13 pages, 10 figures submitted to J. Appl. Phys revised manuscript contains an additional table and some corrections

Journal ref: J. Appl. Phys., Vol. 114, 214501 (2013)

On the work distribution in quasi-static processes

Authors: Johannes Hoppenau, Andreas Engel

Abstract: We derive a systematic, multiple time-scale perturbation expansion for the work distribution in isothermal quasi-static Langevin processes. To first order we find a Gaussian distribution reproducing the result of Speck and Seifert [Phys. Rev. E 70, 066112 (2004)]. Scrutinizing the applicability of perturbation theory we then show that, irrespective of time-scale separation, the expansion breaks do… ▽ More We derive a systematic, multiple time-scale perturbation expansion for the work distribution in isothermal quasi-static Langevin processes. To first order we find a Gaussian distribution reproducing the result of Speck and Seifert [Phys. Rev. E 70, 066112 (2004)]. Scrutinizing the applicability of perturbation theory we then show that, irrespective of time-scale separation, the expansion breaks down when applied to untypical work values from the tails of the distribution. We thus reconcile the result of Speck and Seifert with apparently conflicting exact expressions for the asymptotics of work distributions in special systems and with an intuitive argument building on the central limit theorem. △ Less

Submitted 3 May, 2013; v1 submitted 28 March, 2013; originally announced March 2013.

Comments: 11 pages, 1 figure

Carnot process with a single particle

Authors: Johannes Hoppenau, Markus Niemann, Andreas Engel

Abstract: We determine the statistics of work in isothermal volume changes of a classical ideal gas consisting of a single particle. Combining our results with the findings of Lua and Grosberg [J. Chem. Phys. B 109, 6805 (2005)] on adiabatic expansions and compressions we then analyze the joint probability distribution of heat and work for a microscopic, non-equilibrium Carnot cycle and determine its effici… ▽ More We determine the statistics of work in isothermal volume changes of a classical ideal gas consisting of a single particle. Combining our results with the findings of Lua and Grosberg [J. Chem. Phys. B 109, 6805 (2005)] on adiabatic expansions and compressions we then analyze the joint probability distribution of heat and work for a microscopic, non-equilibrium Carnot cycle and determine its efficiency at maximum power. △ Less

Submitted 24 May, 2013; v1 submitted 1 March, 2013; originally announced March 2013.

Comments: 13 pages, 10 figures

Probing small-scale intermittency with a fluctuation theorem

Authors: D. Nickelsen, A. Engel

Abstract: We characterize statistical properties of the flow field in developed turbulence using concepts from stochastic thermodynamics. On the basis of data from a free air-jet experiment, we demonstrate how the dynamic fluctuations induced by small-scale intermittency generate analogs of entropy-consuming trajectories with sufficient weight to make fluctuation theorems observable at the macroscopic scale… ▽ More We characterize statistical properties of the flow field in developed turbulence using concepts from stochastic thermodynamics. On the basis of data from a free air-jet experiment, we demonstrate how the dynamic fluctuations induced by small-scale intermittency generate analogs of entropy-consuming trajectories with sufficient weight to make fluctuation theorems observable at the macroscopic scale. We propose an integral fluctuation theorem for the entropy production associated with the stochastic evolution of velocity increments along the eddy-hierarchy and demonstrate its extreme sensitivity to the accurate description of the tails of the velocity distributions. △ Less

Submitted 22 May, 2013; v1 submitted 14 December, 2012; originally announced December 2012.

Comments: 5 pages, 3 figures

Journal ref: Phys. Rev. Lett. 110, 214501 (2013)

Temperature-dependence of detection efficiency in NbN and TaN SNSPD

Authors: Andreas Engel, Kevin Inderbitzin, Andreas Schilling, Robert Lusche, Alexei Semenov, Heinz-Wilhelm Hübers, Dagmar Henrich, Matthias Hofherr, Konstantin Il'in, Michael Siegel

Abstract: We present systematic measurements of the temperature-dependence of detection efficiencies in TaN and NbN superconducting nanowire single-photon detectors. We have observed a clear increase of the cut-off wavelength with decreasing temperature that we can qualitatively describe with a temperature-dependent diffusion coefficient of the quasi-particles created after photon absorption. Furthermore, t… ▽ More We present systematic measurements of the temperature-dependence of detection efficiencies in TaN and NbN superconducting nanowire single-photon detectors. We have observed a clear increase of the cut-off wavelength with decreasing temperature that we can qualitatively describe with a temperature-dependent diffusion coefficient of the quasi-particles created after photon absorption. Furthermore, the detection efficiency at wavelengths shorter than the cut-off wavelength as well as at longer wavelengths exhibit distinct temperature dependencies. The underlying causes and possible consequences for microscopic detection models are discussed. △ Less

Submitted 8 January, 2013; v1 submitted 19 October, 2012; originally announced October 2012.

Comments: 5 pages, 3 figures, presented at ASC 2012, accepted for publication in special issue of IEEE Trans. Appl. Supercond. Small changes in text and figures in response to reviewer comments

Journal ref: IEEE Trans. Appl. Supercon., 2013, Vol. 23, 2300505