Nonequilibrium Electron Transport Research Articles

Frontiers, challenges, and solutions in modeling of swift heavy ion effects in materials

Since a few breakthroughs in the fundamental understanding of the effects of swift heavy ions (SHIs) decelerating in the electronic stopping regime in the matter have been achieved in the last decade, it motivated us to review the state-of-the-art approaches in the modeling of SHI effects. The SHI track kinetics occurs via several well-separated stages and spans many orders of magnitude in time: from attoseconds in ion-impact ionization depositing an extreme amount of energy in a target to femtoseconds of electron transport and hole cascades, to picoseconds of lattice excitation and response, to nanoseconds of atomic relaxation, and even longer times of the final macroscopic reaction. Each stage requires its own approaches for quantitative description. We discuss that understanding the links between the stages makes it possible to describe the entire track kinetics within a hybrid multiscale model without fitting procedures. The review focuses on the underlying physical mechanisms of each process, the dominant effects they produce, and the limitations of the existing approaches, as well as various numerical techniques implementing these models. It provides an overview of the ab initio-based modeling of the evolution of the electronic properties, Monte Carlo simulations of nonequilibrium electronic transport, molecular dynamics modeling of atomic reaction including phase transformations and damage on the surface and in the bulk, kinetic Mote Carlo of atomic defect kinetics, and finite-difference methods of track interaction with chemical solvents describing etching kinetics. We outline the modern methods that couple these approaches into multiscale and combined multidisciplinary models and point to their bottlenecks, strengths, and weaknesses. The analysis is accompanied by examples of important results, improving the understanding of track formation in various materials. Summarizing the most recent advances in the field of the track formation process, the review delivers a comprehensive picture and detailed understanding of the phenomenon. Important future directions of research and model development are also outlined.

Current-driven collective dynamics of non-Hermitian edge vibrations in armchair graphene nanoribbons

We study non-Hermitian collective dynamics of spatially separated edge carbon dimer vibrations in armchair graphene nanoribbons, mediated by coherent and dissipative coupling to nonequilibrium electron transport. We show that the indirect coupling between two dimers depends crucially on gating and source-drain bias. In particular, we analyze the competition between two distinctly different energy transfer mechanism from nonequilibrium electrons to vibrations. One is the deterministic work done by nonconservative current-induced force, and the other is stochastic Joule heating. We find that the effect of the former can be effectively tuned electrically through gating and bias. Our work suggests that armchair graphene nanoribbons could serve as promising candidates in the experimental search for signatures of nonconservative current-induced forces in nanoconductors, which remains elusive despite intense theoretical study.

Phonon thermal transport and its tunability in GaN for near-junction thermal management of electronics: A review

The heat dissipation issue has now become one of the most important bottlenecks for power electronics due to the rapid increase in power density and working frequency. Towards the wide bandgap semiconductor GaN high electron mobility transistors (HEMTs), near-junction thermal management is the breakthrough that mainly includes the accurate thermal modeling and effective thermal design for GaN and GaN HEMTs. In this review, we first offer a comprehensive understanding of phonon thermal transport in GaN and GaN HEMTs, including non-equilibrium transport of electrons and phonons in the heat generation process, phonon thermal conductivity, heat spreading, and interfacial thermal transport. Then, we review the current tuning mechanisms and methods for thermal transport in GaN and GaN HEMTs which are classified into three categories according to the particle nature, wave nature, and topological nature of phonons. At last, we conclude by providing our perspectives on challenges and opportunities in the research of phonon thermal transport and its tuning mechanisms in GaN HEMTs.

Ultrafast element- and depth-resolved magnetization dynamics probed by transverse magneto-optical Kerr effect spectroscopy in the soft x-ray range

We report on time- and angle-resolved transverse magneto-optical Kerr effect spectroscopy in the soft x-ray range that, by analysis via polarization-dependent magnetic scattering simulations, allows us to determine the spatio-temporal and element-specific evolution of femtosecond laser-induced spin dynamics in nanostructured magnetic materials. In a ferrimagnetic GdFe thin film system, we correlate a reshaping spectrum of the magneto-optical Kerr signal to depth-dependent magnetization dynamics and disentangle contributions due to non-equilibrium electron transport and nanoscale heat diffusion on their intrinsic time scales. Our work provides a quantitative insight into light-driven spin dynamics occurring at buried interfaces of complex magnetic heterostructures, which can be tailored and functionalized for future opto-spintronic devices.

Local equilibrium charge and spin currents in two-dimensional topological systems

We study the equilibrium and nonequilibrium electronic transport properties of multiprobe topological systems using a combination of the Landauer-B\"uttiker approach and nonequilibrium Green's functions techniques. We obtain general expressions for both nonequilibrium and equilibrium local electronic currents that, by suitable projections, allow one to compute charge, spin, valley, and orbital currents. We show that external magnetic fields give rise to equilibrium charge currents in mesoscopic system and study the latter in the quantum Hall regime. Likewise, a spin-orbit interaction leads to local equilibrium spin currents, that we analyze in the quantum spin Hall regime. We show that an accurate theoretical assessment of the equilibrium currents is quite challenging and propose a two-measurement protocol that facilitates a comparison between experiment and theory.

Unified Formulation of Phase Space Mapping Approaches for Nonadiabatic Quantum Dynamics.

Nonadiabatic dynamical processes are one of the most important quantum mechanical phenomena in chemical, materials, biological, and environmental molecular systems, where the coupling between different electronic states is either inherent in the molecular structure or induced by the (intense) external field. The curse of dimensionality indicates the intractable exponential scaling of calculation effort with system size and restricts the implementation of "numerically exact" approaches for realistic large systems. The phase space formulation of quantum mechanics offers an important theoretical framework for constructing practical approximate trajectory-based methods for quantum dynamics. This Account reviews our recent progress in phase space mapping theory: a unified framework for constructing the mapping Hamiltonian on phase space for coupled F-state systems where the renowned Meyer-Miller Hamiltonian model is a special case, a general phase space formulation of quantum mechanics for nonadiabatic systems where the electronic degrees of freedom are mapped onto constraint space and the nuclear degrees of freedom are mapped onto infinite space, and an isomorphism between the mapping phase space approach for nonadiabatic systems and that for nonequilibrium electron transport processes. While the zero-point-energy parameter is conventionally assumed to be positive, we show that the constraint implied in the conventional Meyer-Miller mapping Hamiltonian requires that such a parameter can be negative as well and lies in (-1/F, +∞) for each electronic degree of freedom. More importantly, the zero-point-energy parameter should be interpreted as a special case of a commutator matrix in the comprehensive phase space mapping Hamiltonian for nonadiabatic systems. From the rigorous formulation of mapping phase space, we propose approximate but practical trajectory-based nonadiabatic dynamics methods. The applications to both gas phase and condensed phase problems include the spin-boson model for condensed phase dissipative two-state systems, the three-state photodissociation models, the seven-site model of the Fenna-Matthews-Olson monomer in photosynthesis of green sulfur bacteria, the strongly coupled molecular/atomic matter-optical cavity systems designed for controlling and manipulating chemical dynamical processes, and the Landauer model for a quantum dot state coupled with two electrodes. In these applications the overall performance of our phase space mapping dynamics approach is superior to two prevailing trajectory-based methods, Ehrenfest dynamics and fewest switches surface hopping.

Local Nonequilibrium Electron Transport in Metals after Femtosecond Laser Pulses: A Multi-Temperature Hyperbolic Model

ABSTRACT The trend toward miniaturization of electronic devices has increased the interest in nano scale heat transport, particularly, in laser-excited solids where electron–electron thermalization and electron-phonon coupling play a key role. Using a multi-temperature hyperbolic model, which takes into account the coupling between initially non-thermalized electrons and different phonon branches, we obtain a hierarchy of heat conduction equations for the electron temperature, which arises due to multi-length and time scales nature of coupling between different excitations. The hierarchy predicts that the ultrashort laser pulse induces a multi-front temperature wave propagating into the bulk of the material, which includes various heat transport regimes, ranging from the ballistic motion of the initially non-thermalized electrons propagating on the shortest time scale without interaction with the lattice as a temperature discontinuity, to the continuous wave-like temperature fronts arising on the intermediate time scale due to coupling between various excitations, and eventually to the classical Fourier transport on the longest time scale. The model is expected to be useful for modeling heat wave propagation phenomena in heterostructures and metamaterials.

First-principles nonequilibrium dynamical cluster theory for quantum transport simulations of disordered nanoelectronic devices

As important progress for simulating realistic device materials, we report the first-principles nonequilibrium dynamical cluster theory for simulating the quantum transport properties of nanoelectronics with inevitable disordered defects or dopants. In this method, we formulate the nonequilibrium dynamical cluster theory in Keldysh's Green's function representation, and implement it with the exact muffin-tin orbital based density functional theory. With this method, the important correlation effects of disordered scattering and short-range order effects can be effectively treated for the nonequilibrium electronic structure and quantum transport calculations of devices under finite bias. Moreover, a double-energy-contour technique is devised to considerably improve the numerical convergence in the nonequilibrium electron structure calculation. As the demonstration, the first-principles nonequilibrium dynamical cluster theory is applied to calculate Cu/Co junction with disordered interface and Fe/vacuum/Fe magnetic tunnel junction with surface roughness. We find that a sizable transmission decrease can be induced by including the correlation effects of disorders of few layers in the Cu/Co junction, presenting the important transport channel closing due to disordered quantum interference. For Fe/vacuum/Fe junction, we find that short-range order of surface roughness, with the important clustering and anticlustering tendencies, can dramatically change the transmission properties compared to the case of (or close to) complete randomness. The development of first-principles nonequilibrium dynamical cluster theory provides an important approach for analyzing the process-dependent device performance, extending the capability of first-principles quantum transport simulation.

Coupling Nonequilibrium Electron Transport with Maxwell Equations for Modelling Nonlinear Optical Properties

Numerical approach to modelling nonlinear optical properties is presented. The model is based on a self-consistent solution of the Boltzmann transport equation for electrons and the Maxwell equations.

Electron-phonon drag enhancement of transport properties from a fully coupled ab initio Boltzmann formalism

We present a combined treatment of the non-equilibrium dynamics and transport of electrons and phonons by carrying out \textit{ab initio} calculations of the fully coupled electron and phonon Boltzmann transport equations. We find that the presence of mutual drag between the two carriers causes the thermopower to be enhanced and dominated by the transport of phonons, rather than electrons as in the traditional semiconductor picture. Drag also strongly boosts the intrinsic electron mobility, thermal conductivity and the Lorenz number. Impurity scattering is seen to suppress the drag-enhancement of the thermal and electrical conductivities, while having weak effects on the enhancement of the Lorenz number and thermopower. We demonstrate these effects in \textit{n}-doped 3C-SiC at room temperature, and explain their origins. This work establishes the roles of microscopic scattering mechanisms in the emergence of strong drag effects in the transport of the interacting electron-phonon gas.

NanoNET: An extendable Python framework for semi-empirical tight-binding models

We present a novel open-source Python framework called NanoNET (Nanoscale Non-equilibrium Electron Transport) for modeling electronic structure and transport. Our method is based on the tight-binding method and non-equilibrium Green’s function theory. The core functionality of the framework is providing facilities for efficient construction of tight-binding Hamiltonian matrices from a list of atomic coordinates and a lookup table of the two-center integrals in dense, sparse, or block-tridiagonal forms. The framework implements a method based on kd-tree nearest-neighbor search and is applicable to isolated atomic clusters and periodic structures. A set of subroutines for detecting the block-tridiagonal structure of a Hamiltonian matrix and splitting it into series of diagonal and off-diagonal blocks is based on a new greedy algorithm with recursion. Additionally the developed software is equipped with a set of programs for computing complex band structure, self-energies of elastic scattering processes, and Green’s functions. Examples of usage and capabilities of the computational framework are illustrated by computing the band structure and transport properties of a silicon nanowire as well as the band structure of bulk bismuth. Program summaryProgram Title:NanoNETCPC Library link to program files:https://doi.org/10.17632/b9p7kyzdj9.1Developer’s repository link:https://github.com/freude/NanoNetLicensing provisions: MITProgramming language: PythonNature of problem: The framework NanoNET solves a problem which is, having a set of atomic coordinates and tight-binding parameters, to construct Hamiltonian matrices in one of several desired forms. In particular, some applications require those matrices to have a reduced bandwidth and/or to possess a block-tridiagonal structure.Solution method: The problem is solved using a combination of kd-tree-based fast nearest-neighbor search and atomic coordinate sorting. Furthermore, a new greedy recursive algorithm is proposed for detecting block-tridiagonal structure of a matrix in a non-optimal way. Additionally, we propose an algorithm of a polynomial time for optimizing block sizes.Additional features: Although the resulting matrices can be processed by many existing software packages, the framework also has built-in standard tools for diagonalizing Hamiltonian matrices and computing Green’s functions that make it an independent tool for solving electronic structure and transport problems.

Non-equilibrium electronic transport through a quantum dot with strong Coulomb repulsion in the presence of a magnetic field

The non-equilibrium electronic transport through a nanoscale device composed of a single quantum dot between two metallic contacts is studied theoretically within the framework of the Keldysh formalism. The quantum dot consists of a single energy level subject to an applied magnetic field. Correlations due to the Coulomb repulsion between electrons on the dot are treated with a Green’s function decoupling scheme which, although similar to the Hubbard-I approximation, captures some of the dynamics beyond. The scheme is exact in the so-called atomic limit, defined by vanishing tunneling between contacts and dot, and in the non-interacting limit, where the on-dot Coulomb repulsion is zero. Explicit analytic solutions, valid for arbitrary magnetic fields, are obtained for two important setups: (i) the stationary regime, with constant voltage bias between the leads, and (ii) the time-dependent regime for metallic leads with constant density of states of infinite width. In these regimes, the current through the dot is evaluated numerically for various parameter sets and its main features interpreted in terms of the underlying physical processes. The results are compared to the non-crossing approximation (NCA) and diagrammatic non-equilibrium quantum Monte-Carlo (QMC) where available.

New horizons in thermoelectric materials: Correlated electrons, organic transport, machine learning, and more

Thermoelectrics represent a unique opportunity in energy to directly convert thermal energy or secondary waste heat into a primary resource. The development of thermoelectric materials has improved over the decades in leaps, rather than by increments—each leap forward has recapitulated the science of its time: from the crystal growth of semiconductors, to controlled doping, to nanostructuring, and to 2D confinement. Each of those leaps forward was, arguably, more a result of materials science than physics. Thermoelectrics is now ripe for another leap forward, and many probable advances rely on new physics outside of the standard band transport model of thermoelectrics. This perspective will cover a limited selection of how thermoelectrics can benefit from new discoveries in physics: wave effects in phonon transport, correlated electron physics, and unconventional transport in organic materials. We also highlight recent developments in thermoelectrics discovery aided by machine learning that may be needed to realize some of these new concepts practically. Looking ahead, developing new thermoelectric physics will also have a concomitant domino effect on adjacent fields, furthering the understanding of nonequilibrium thermal and electronic transport in novel materials.

Electronic transport properties of silicon chains sandwiched between graphene electrodes: first-principles study

ABSTRACTThe effects of orientation and silicon chain length on the electronic transport properties for linear silicon chains sandwiched between two graphene electrodes are investigated by using non-equilibrium Green’s functions combined with density functional theory. Our results demonstrate that the conductance of single silicon chains can hardly be affected by its orientation, as there is negligible difference between the conductance of tilted and un-tilted chains, and the conductance is impacted greatly by the length of chains, i.e. the transmission coefficient is doubled for double chains. The equilibrium conductance of single silicon chains shows even-odd oscillating behavior, and its tendency decreases with the increase of the chain length. The non-equilibrium electronic transport properties for all types of chains are also calculated, and all current–voltage curves of silicon chains show a linear character. The frontier molecular orbitals, the total and projected density of states are used to analyse the electronic transport properties for all types of chains.

Analysis of Nonequilibrium Transport Properties of Interacting Quantum Wire Models

We analyze nonequilibrium electronic transport properties of a typical interacting three-site quantum wire model within Hartree-Fock approximation making use of Keldysh formalism. Some rigorous formulas are provided for direct calculations when Coulomb repulsion is present. According to numerical calculations using above formulas, we investigate the conductance, transport currents, and on site electronic charges of the wire on some special occasions in the interacting case, and also compare them with the results in the noninteracting case.

Photoinduced Nonequilibrium Topological States in Strained Black Phosphorus.

Black phosphorus (BP), an elemental semiconductor, has attracted tremendous interest because it exhibits a wealth of interesting electronic and optoelectronic properties in equilibrium condition. The nonequilibrium electronic structures of bulk BP under a periodic field of laser remain unexplored, but can lead to intriguing topological optoelectronic properties. Here we show that, under the irradiation of circularly polarized light (CPL), BP exhibits a photon-dressed Floquet-Dirac semimetal state, which can be continuously tuned by changing the direction, intensity, and frequency of the incident laser. The topological phase transition from type-I to type-II Floquet-Dirac fermions manifests a new form of type-III phase, which exists in a wide range of intensities and frequencies of the incident laser. Furthermore, topological surface states exhibit nonequilibrium electron transport in a direction locked by the helicity of CPL. Our findings not only deepen our understanding of fundamental properties of BP in relation to topology but also extend optoelectronic device applications of BP to the nonequilibrium regime.

Enhancing optical response of graphene through stochastic resonance

Enhancing the optical response of graphene is a topic of interest with applications in optoelectronics. Subject to light irradiation, graphene can exhibit nontrivial topologically insulating states, effectively turning itself into a Floquet topological insulator due to the time periodicity of the external driving. We find that, when random disorder is present, its interplay with the topologically insulating states can have a dramatic effect on electronic transport through graphene. In particular, we consider the prototypical setting where a graphene nanoribbon is irradiated by circularly polarized light, where the length of the nanoribbon is sufficiently long so that evanescent states have little effect on transport. We uncover a resonance phenomenon in which the conductance is enhanced as the disorder strength is increased from zero, reaches a maximum value for an optimal level of disorder, and decreases as the disorder is strengthened further. With respect to its value at the zero-disorder strength, the maximum conductance value can be as much as $50%$ higher. Qualitatively, this can be understood as a result of the dynamical interplay between disorder and Floquet states (channels) generated by light irradiation. Quantitatively, the resonance phenomenon can be explained in the framework of Born theory, where the disorder reorganizes the Floquet Hamiltonian and enhances the effective coupling between the adjacent Floquet conducting channels. That is, disorder is capable of promoting both photon absorption and emission, leading to significant enhancement of nonequilibrium electronic transport. We demonstrate the robustness of the resonance phenomenon by investigating the effects of spatial symmetry breaking on transport and provide an understanding based on analyzing the behavior of the density of states of the Floquet channels.

Non-equilibrium electron transport induced by terahertz radiation in the topological and trivial phases of Hg1-x Cd x Te.

Terahertz photoconductivity in heterostructures based on n-type Hg1−xCdxTe epitaxial films both in the topological phase (x < 0.16, inverted band structure, zero band gap) and the trivial state (x > 0.16, normal band structure) has been studied. We show that both the positive photoresponse in films with x < 0.16 and the negative photoconductivity in samples with x > 0.16 have no low-energy threshold. The observed non-threshold positive photoconductivity is discussed in terms of a qualitative model that takes into account a 3D potential well and 2D topological Dirac states coexisting in a smooth topological heterojunction.

Injection of emitted electrons in a multigrained semiconductor nanostructure

The mechanism of injection of emitted electrons into submicron grains of semiconductors has been studied by approximating their experimental current–voltage (I–V) characteristics. It is concluded that the injection in both single-crystalline and multigrained semiconductor structure can be described by the same physical model based on the notions of electron tunneling via the surface barrier and diffusion-drift transport of nonequilibrium electrons in the semiconductor. A determining role belongs to the I–V characteristic described by a power law with exponents from 2 to 4. Analysis of I–V curves allows the product of mobility and diffusion length of nonequilibrium electrons to be estimated. The obtained results can be used in the investigation and creation of multigrained semiconductor structures for gas sensors, optical sensors, and detectors and sources of infrared and terahertz radiation.

Distinctive electronic transport in pyridine-based devices with narrow graphene nanoribbon electrodes

Two kinds of pyridine-based molecular devices with the same narrow ZGNR electrodes show different and distinctive non-equilibrium electron transport properties.