We present an atomistic quantum transport simulation framework based on the Non-Equilibrium Green's Function (NEGF) formalism to model impact ionization in semiconductor avalanche devices, with direct relevance to near-term quantum networking applications. Conventional descriptions of avalanche breakdown rely predominantly on semiclassical simulation methods, such as local ionization coefficients, semiclassical carrier trajectories, or Monte Carlo sampling, all of which implicitly assume weak correlations and mean-field electronic interactions. These assumptions break down in nanoscale, high-field junctions where carrier multiplication emerges from strongly non-equilibrium, energy-resolved scattering processes.
Our approach formulates impact ionization as a multi-particle self-energy within NEGF, enabling a non-perturbative, energy- and atomic orbital-resolved description of carrier multiplication directly from the device spectral function. This formulation captures strongly inelastic scattering processes beyond semiclassical approximations and is implemented in a matrix-based real-space representation suitable for nanoscale device modeling. Using a model semiconductor structure under high electric fields, we demonstrate the emergence of carrier multiplication and analyze its dependence on energy-resolved transport and nonequilibrium charge distributions. The framework provides insight into microscopic mechanisms governing avalanche processes and their impact on device performance. Our results establish a transport baseline for self-consistent calculations of the impact-ionization self-energy and carrier multiplication. By resolving the available and occupied states that underlie avalanche onset, this framework provides a route toward predictive modeling of silicon single-photon avalanche detectors and avalanche photodiodes used in quantum-network receivers.
Comments
12 pages, 8 figures; submitted to the IEEE QCE26 conference
We present an atomistic quantum transport simulation framework based on the Non-Equilibrium Green's Function (NEGF) formalism to model impact ionization in semiconductor avalanche devices, with direct relevance to near-term quantum networking applications. Conventional descriptions of avalanche breakdown rely predominantly on semiclassical simulation methods, such as local ionization coefficients, semiclassical carrier trajectories, or Monte Carlo sampling, all of which implicitly assume weak correlations and mean-field electronic interactions. These assumptions break down in nanoscale, high-field junctions where carrier multiplication emerges from strongly non-equilibrium, energy-resolved scattering processes.
Our approach formulates impact ionization as a multi-particle self-energy within NEGF, enabling a non-perturbative, energy- and atomic orbital-resolved description of carrier multiplication directly from the device spectral function. This formulation captures strongly inelastic scattering processes beyond semiclassical approximations and is implemented in a matrix-based real-space representation suitable for nanoscale device modeling. Using a model semiconductor structure under high electric fields, we demonstrate the emergence of carrier multiplication and analyze its dependence on energy-resolved transport and nonequilibrium charge distributions. The framework provides insight into microscopic mechanisms governing avalanche processes and their impact on device performance. Our results establish a transport baseline for self-consistent calculations of the impact-ionization self-energy and carrier multiplication. By resolving the available and occupied states that underlie avalanche onset, this framework provides a route toward predictive modeling of silicon single-photon avalanche detectors and avalanche photodiodes used in quantum-network receivers.
We investigate memory effects and quantum transport in two-dimensional lattice systems within the framework of non-equilibrium Green's functions and Schwinger-Keldysh non-equilibrium quantum field theory. Starting from a 2D tight-binding Hamiltonian, we employ the Dyson expansion on the Keldysh contour and the second-order Born and self-consistent Born Approximation to derive the electronic self-energies associated with elastic and inelastic scattering mechanisms.Static disorder produces a local self-energy and a rapidly decaying memory kernel, characteristic of Markovian dynamics, whereas electron-phonon coupling generates temporally nonlocal self-energies and genuine Non-Markovian behavior. We demonstrate that these distinct memory signatures are directly reflected in the spectral function, which we propose as a diagnostic probe of non-equilibrium memory effects. Further we explore 1PI and 2PI effective actions to see their memory perspectives studying their coarse-graining behavior. Building on this theoretical framework, we further apply the conventional NEGF formalism to two paradigmatic two-dimensional models-the Hofstadter and an RKKY-coupled system to explore how different microscopic Hamiltonians influence Markovian and Non-Markovian nature. Our results provide a unified connection between scattering mechanisms, memory effects, and quantum transport in low-dimensional systems.
As experimental probes have matured to observe ultrafast transient and high frequency responses of materials and devices, so to have the theoretical methods to numerically and analytically simulate time- and frequency-resolved transport. In this review article, we discuss recent progress in the development of the time-dependent and frequency-dependent non-equilibrium Green function (NEGF) technique. We begin with an overview of the theoretical underpinnings of the underlying Kadanoff-Baym equations and derive the fundamental NEGF equations in the time and frequency domains. We discuss how these methods have been applied to a variety of condensed matter systems such as molecular electronics, nanoscale transistors, and superconductors. In addition, we survey the application of NEGF in fields beyond condensed matter, where it has been used to study thermalization in ultra-cold atoms and to understand leptogenesis in the early universe. Throughout, we pay special attention to the challenges of incorporating contacts and interactions, as the NEGF method is uniquely capable of accounting for such features.
The method of nonequilibrium Green functions (NEGFs) constitutes a solid framework to describe closed and open quantum systems. It captures situations far from equilibrium including arbitrary perturbations and correlations - effects higher than first order in the binary interactions. On the contrary, in the absence of external fields, it reduces to the imaginary-time Matsubara formalism. The abilities (and successes) of the method originate from its self-consistency and the conserving character of many-body approximations that are introduced by diagram technique. On this account, NEGFs have, now for a long time, brought insight into the dynamics of nuclear matter, non-ideal quantum gases and (semiconductor) plasmas. However, applications to localized, finite and strongly interacting systems have emerged only within the recent decade. The dynamical properties follow from quantum kinetic equations - the two-time Kadanoff-Baym equations for the one-particle NEGF - the numerical solution of which is the central topic of this thesis. The non-Markovian structure of these equations thereby inhibits an unlimited, gradual propagation of the nonequilibrium Green function: Any self-consistent, future dynamics of the system is tightly linked to the (complete) past by non-local self-energies. Further, the success in obtaining solutions is being diminished if the system under investigation is not isotropic or inhomogeneous and, in addition, the spatial topology (e.g., the charge carrier or spin density) needs to be resolved in time. On top of this, small isolated systems are generally not candidates showing fast decoherence which offers little hope for smooth and well-damped integration kernels. Despite these difficulties, the thesis at hand is devoted to the computation of the two-time NEGF for finite, closed systems of which ensembles of electrons bound by nuclei forming atoms or molecules are the most natural representatives. Here, in the spirit of the well-studied one-dimensional helium atom, the electron dynamics in model atoms and molecules is addressed in ab initio fashion. To render calculations possible in the first place, (i) a novel hybrid representation of the NEGF is introduced based on the conception of finite elements (FE) and the discrete variable representation (DVR), and (ii) a parallel algorithm is developed that allows for an efficient, well scalable distributed-memory computation of the full two-time Green function. The first point attributes plenty of flexibility and makes the method readily adjustable to different Hamiltonians avoiding the need to, by hand or in intricate numerical manner, calculate the whole bunch of matrix elements of one- and two-particle operators. Also, in consequence, it drastically simplifies the evaluation of self-energies. The second point makes the NEGF approach ready for large-scale, high-performance computing facilities, the resources (of computer power: mainly memory!) of which are indispensable for (some of) the calculations presented. The applicability of the developed methods is demonstrated inter alia on the basis of helium, beryllium, hydrogen and lithium hydride modeled in one spatial dimension whereby electron-electron correlations are treated in the second(-order) Born approximation. After a thorough discussion on the self-consistent ground states, the thesis focuses on the electron dynamics in the linear response regime as well as in the presence of strong external fields. Overall, to assess the the performance of the second Born approximation, the results are compared to the Hartree-Fock approximation, on the one hand, and to the exact solution of the time-(in)dependent Schrödinger equation, on the other hand. In addition, aiming at the possibility of extended time-dependent calculations, the behavior of the generalized Kadanoff-Baym ansatz is discussed.
The method of nonequilibrium Green functions (NEGFs) constitutes a solid framework to describe closed and open quantum systems. It captures situations far from equilibrium including arbitrary perturbations and correlations - effects higher than first order in the binary interactions. On the contrary, in the absence of external fields, it reduces to the imaginary-time Matsubara formalism. The abilities (and successes) of the method originate from its self-consistency and the conserving character of many-body approximations that are introduced by diagram technique. On this account, NEGFs have, now for a long time, brought insight into the dynamics of nuclear matter, non-ideal quantum gases and (semiconductor) plasmas. However, applications to localized, finite and strongly interacting systems have emerged only within the recent decade. The dynamical properties follow from quantum kinetic equations - the two-time Kadanoff-Baym equations for the one-particle NEGF - the numerical solution of which is the central topic of this thesis. The non-Markovian structure of these equations thereby inhibits an unlimited, gradual propagation of the nonequilibrium Green function: Any self-consistent, future dynamics of the system is tightly linked to the (complete) past by non-local self-energies. Further, the success in obtaining solutions is being diminished if the system under investigation is not isotropic or inhomogeneous and, in addition, the spatial topology (e.g., the charge carrier or spin density) needs to be resolved in time. On top of this, small isolated systems are generally not candidates showing fast decoherence which offers little hope for smooth and well-damped integration kernels. Despite these difficulties, the thesis at hand is devoted to the computation of the two-time NEGF for finite, closed systems of which ensembles of electrons bound by nuclei forming atoms or molecules are the most natural representatives. Here, in the spirit of the well-studied one-dimensional helium atom, the electron dynamics in model atoms and molecules is addressed in ab initio fashion. To render calculations possible in the first place, (i) a novel hybrid representation of the NEGF is introduced based on the conception of finite elements (FE) and the discrete variable representation (DVR), and (ii) a parallel algorithm is developed that allows for an efficient, well scalable distributed-memory computation of the full two-time Green function. The first point attributes plenty of flexibility and makes the method readily adjustable to different Hamiltonians avoiding the need to, by hand or in intricate numerical manner, calculate the whole bunch of matrix elements of one- and two-particle operators. Also, in consequence, it drastically simplifies the evaluation of self-energies. The second point makes the NEGF approach ready for large-scale, high-performance computing facilities, the resources (of computer power: mainly memory!) of which are indispensable for (some of) the calculations presented. The applicability of the developed methods is demonstrated inter alia on the basis of helium, beryllium, hydrogen and lithium hydride modeled in one spatial dimension whereby electron-electron correlations are treated in the second(-order) Born approximation. After a thorough discussion on the self-consistent ground states, the thesis focuses on the electron dynamics in the linear response regime as well as in the presence of strong external fields. Overall, to assess the the performance of the second Born approximation, the results are compared to the Hartree-Fock approximation, on the one hand, and to the exact solution of the time-(in)dependent Schrödinger equation, on the other hand. In addition, aiming at the possibility of extended time-dependent calculations, the behavior of the generalized Kadanoff-Baym ansatz is discussed.
Abstract We review one of the most versatile theoretical approaches to the study of time-dependent correlated quantum transport in nano-systems: the non-equilibrium Green’s function (NEGF) formalism. Within this formalism, one can treat, on the same footing, inter-particle interactions, external drives and/or perturbations, and coupling to baths with a (piece-wise) continuum set of degrees of freedom. After a historical overview on the theory of transport in quantum systems, we present a modern introduction of the NEGF approach to quantum transport. We discuss the inclusion of inter-particle interactions using diagrammatic techniques, and the use of the so-called embedding and inbedding techniques which take the bath couplings into account non-perturbatively. In various limits, such as the non-interacting limit and the steady-state limit, we then show how the NEGF formalism elegantly reduces to well-known formulae in quantum transport as special cases. We then discuss non-equilibrium transport in general, for both particle and energy currents. Under the presence of a time-dependent drive—encompassing pump–probe scenarios as well as driven quantum systems—we discuss the transient as well as asymptotic behavior, and also how to use NEGF to infer information on the out-of-equilibrium system. As illustrative examples, we consider model systems general enough to pave the way to realistic systems. These examples encompass one- and two-dimensional electronic systems, systems with electron–phonon couplings, topological superconductors, and optically responsive molecular junctions where electron–photon couplings are relevant.
The framework of nonequilibrium Green functions (NEGFs) is developed to accurately describe interacting quantum systems evolving in the presence of strongly exciting ultra-fast fields.At its core stands the selfconsistent determination of the selfenergy, a functional of the single-particle Green function, which incorporates all relevant many-body physics and, via diagrammatic techniques, guarantees the conservation of the constants of motion.Over the last decades, NEGFs have been successfully applied to a broad range of domains ranging from homogeneous systems such as non-ideal quantum gases and plasmas over condensed matter to highly inhomogeneous systems such as atoms and molecules photo-ionized by laser-fields or colliding nuclear matter.Only recently, the first accurate simulation of the expansion dynamics of clouds of ultra-cold fermionic atoms in a two-dimensional optical lattice could be achieved using NEGFs.The single-particle Green function is the solution of a coupled set of kinetic equations.Its intrinsic dependence on two independent time-arguments, ranging over the complete past of the system, not only enables the determination of all singleparticle observables but also provides access to important two-particle observables and spectral information.With this coupling to the history, though, comes the practical necessity to apply physically motivated approximation techniques to the structure of the selfenergy and the Green functions, to achieve numerical tractability.This thesis is devoted to provide a thorough overview of the possible approximation techniques including perturbative and non-perturbative approaches.Starting from the exact coupled set of equations of motion for the Green functions, the expressions for all selfenergy approximations are derived in the most general basis representation, i.e., for interaction tensor elements w ijkl .From this, the corresponding expressions in a diagonal basis, where the interaction can be described as a matrix w ij , and for the special case of the Hubbard model, where the interaction is just given as a scalar U , are deduced.