Quantum transport phenomena induced by time-dependent fields

We develop a comprehensive framework for characterizing fluctuations in quantum transport and nonequilibrium thermodynamics using two complementary approaches: full counting statistics and first-passage times. Focusing on open quantum systems governed by Markovian Lindblad dynamics, we derive general ensemble relations that connect the two approaches at all times, and we clarify how the steady states reached at long times relate to those reached at large jump counts. In regimes of metastability, long-lived intermediate states cause violations of experimentally testable cumulant relations, as we discuss. We also formulate a fluctuation theorem governing the probability of rare fluctuations in the first-passage time distributions based on results from full counting statistics. Our results apply to general integer-valued trajectory observables that do not necessarily increase monotonically in time. Three illustrative applications, a two-state emitter, a driven qubit, and a variant of the Su-Schrieffer-Heeger model, highlight the physical implications of our results and provide guidelines for practical calculations. Our framework provides a complete picture of first-passage time statistics in Markovian quantum systems, encompassing multiple earlier results, and it has direct implications for current experiments in quantum optics, superconducting circuits, and nanoscale heat engines.

The interaction with time-dependent external fields, especially the interplay between time-dependent driving and quantum correlations, changes the familiar picture of electron transport through nanoscale systems. Although the exact solution of the problem of AC quantum transport of noninteracting electrons has been known for more than two decades, the treatment of correlated particles presents a significant theoretical challenge. In this paper, using the perturbative separation of fast electron tunnelling and slow driving time-scales, we developed a practical approach for time-dependent quantum transport with nonequilibrium Green's functions. The fast electronic dynamics is associated with relative time whilst the slow driving is related to the central time in the Green's functions. The ratio of characteristic electron tunneling time over the period of harmonic driving is used as a small parameter in the theory to obtain a convergent time-derivative expansions of the Green's functions. This enables the algebraic solution of the Kadanoff-Baym equations in Wigner space. Consequently, we produced analytical expressions for dynamical corrections to advanced, retarded, and lesser Green's functions, as well as an improved expression for AC electric current. The method developed is applicable to the general case of multi-channel electron transport through a correlated central region. The theory is applied to different transport scenarios: time-dependent transport through a driven single-resonant level is compared to exact results; and electron transport through a molecular junction described by the Holstein model with a time-oscillating voltage bias is also investigated.

Topological matters include topological insulator, topological semimetal and topological superconductor. The topological semimetals are three-dimensional topological states of matter with gapless electronic excitations. They are simply divided into Weyl, Dirac, and nodal-line semimetals according to the touch type of the conduction band and the valence band. Their characteristic electronic structures lead to topologically protected surface states at certain surfaces, corresponding to the novel transport properties. We review our recent works on quantum transport mainly in topological semimetals. The main theories describing the transport behavior of topological matters are given in different magnetic regions.

A determinist method is presented for solving the steady-state Wigner transport equation in nanoscale MOSFET devices. The three-dimensional quantum transport is computed by solving the coupled 3D Poisson and 2D Schrödinger equations (by a mode-space approach) with the 1D Wigner transport equation along the source-drain direction. Numerical simulations are performed to demonstrate the ability of the Wigner function formalism to correctly reproduce quantum transport properties in gate-all-around silicon nanowire MOSFETs.

As MOSFET channel lengths approach the nanoscale, the reliability of semi-classical transport models decreases. To offer additional insight into transport phenomena in these deeply scaled devices, simulation tools that treat quantum transport without sacrificing the realistic treatment of scattering are needed. A unique non-equilibrium Green's function approach Schrodinger Equation Monte Carlo (SEMC) has been developed that provides a physically rigorous approach to quantum transport and phase-breaking inelastic scattering via real (actual) scattering processes such as optical and acoustic phonon scattering. Quasi-one-dimensional SEMC codes previously have been applied to study essential quantum transport physics in devices such as quantum well lasers where the potential varies only along the nominal direction of transport, although with a fully three-dimensional (3D) treatment of scattering. However, such 1D analysis cannot provide quantitatively accurate results for 2D MOSFET structures, and, in particular, lacks the capability of self-consistency with respect to the potential profile. In this paper, the development of a SEMC-2D code for electrostatically self-consistent treatment of quantum transport within devices with, additionally, quantum confinement normal to the direction of transport, is reported along with illustrative simulation results for nano-scaled SOI MOSFETs geometries.

Topological matters include topological insulator, topological semimetal and topological superconductor. The topological semimetals mainly concerned in this paper are three-dimensional topological states of matter. They are simply divided into Weyl, Dirac, and nodal-line semimetals according to the touch type of the conduction band and the valence band, and genalrally have topologically protected Fermi arcs at certain surfaces. We review our recent works on quantum transport in topological semimetals, according to the strength of the magnetic field. Near zero magnetic fields, there are competitions between the positive magnetoresistivity induced by the weak anti-localization effect and negative magnetoresistivity related to the nontrivial Berry curvature. We propose a fitting formula for the magnetoconductivity of the weak anti-localization. We expect that the weak localization may be induced by inter-valley effects and interaction effect, and occur in double-Weyl semimetals. We propose the conductivity correction

As MOSFET channel lengths approach the nanoscale, the reliability of semi-classical models of transport decreases. However, we have not yet, nor perhaps ever will we, reach the point where effects related to scattering such as mobility degradation and electrostatic screening can be neglected. To offer additional insight into transport phenomena in these deeply scaled devices, simulation tools that treat quantum transport without sacrificing the realistic treatment of scattering are needed. In recent years we and colleagues have been developing a unique non-equilibrium Green's function approach Schrodinger Equation Monte Carlo (SEMC) that provides a physically rigorous approach to quantum transport and phase-breaking inelastic scattering via real (actual) scattering processes such as optical and acoustic phonon scattering. Quasi-one-dimensional SEMC codes previously have been applied to model transport in systems such as quantum well lasers where the potential varies only along the nominal direction of transport, although with a fully three-dimensional (3D) treatment of scattering. In this paper, the development of a SEMC-2D code for electrostatically self-consistent treatment of quantum transport within devices with, additionally, quantum confinement normal to the direction of transport, is reported along with illustrative simulation results for nano-scaled SOI MOSFETs geometries.

Transport phenomena are fundamental to understanding and optimizing quantum systems. This study investigates the transport properties of multidot quantum systems configured in series and parallel combinations, emphasizing two key aspects: the Wiedemann-Franz (WF) law and the Thermodynamic Uncertainty Relation (TUR). Using the scattering approach within the linear response framework, we analyze transmission functions, thermoelectric properties, and TUR. A general expression for quantum corrections under constant transmission conditions, where electron tunneling is probabilistic, is derived. Our findings reveal critical insights: (i) quantum phase transitions between weak and strong coupling regimes in parallel configurations, (ii) consistent violations of the WF law across all systems, and (iii) adherence to the TUR in the presence of the Aharonov-Bohm (AB) phase. Additionally, we report distinctive behaviors in transmission and thermoelectric properties, including charge and thermal conductance, the Lorenz ratio, and thermopower. For both constant and phase-dependent transmission scenarios, the TUR value consistently satisfies thresholds, and quantum corrections remain positive, underscoring their robustness. These results advance the understanding of quantum transport and provide a framework for optimizing performance in multidot quantum systems.

With this work we investigate the stationary nonequilibrium density matrix of current carrying nonequilibrium steady states of in-between quantum systems that are connected to reservoirs. We describe the analytical procedure to obtain the explicit result for the reduced density matrix of quantum transport when the system, the connecting reservoirs, and the system-reservoir interactions are described by quadratic Hamiltonians. Our procedure is detailed for both electronic transport described by the tight-binding Hamiltonian and for phonon transport described by harmonic Hamiltonians. For the special case of weak system-reservoir couplings, a more detailed description of the steady-state density matrix is obtained. Several paradigm transport setups for interelectrode electron transport and low-dimensional phonon heat flux are elucidated.

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.

It has been well established that the evolution of an isolated quantum system can appear as undergoing pure dephasing to an observer using an imperfect clock. In this work, we apply this theory to the transport phenomenon in open quantum systems. Starting with a system intrinsically undergoing nonunitary evolution in ideal time, we consider the effect of a realistic clock that approaches Gaussian distribution in the long-time limit. For quantum transport, it eventually leads to a general physical prediction: a stable probability current in a quantum transport system must be robust against any transformation that conforms with a simple formula given by an ideal Gaussian stationary clock. This understanding of quantum transport is demonstrated numerically in a topological insulator, where it also explains the robustness of the quantum Hall response against pure dephasing.

We consider the problem of energy transport in a chain of coupled dissipative quantum systems in the presence of non-Markovian dephasing. We use a model of non-Markovianity which is experimentally realizable in the context of controlled quantum systems. We show that non-Markovian dephasing can significantly enhance quantum transport, and we characterize this phenomenon in terms of internal coupling strengths of the chain for some chain lengths. Finally, we show that the phenomenon of dephasing-assisted quantum transport is also enhanced in the non-Markovian scenario when compared to the Markovian case. Our work brings together engineered environments, which are a reality in quantum technologies, and energy transport, which is typically discussed in terms of complex molecular systems. We then expect that it may motivate experimental work and further theoretical investigations on resources which can enhance transport efficiency in a controllable way. This can help in the design of quantum devices with lower dissipation rates, an important concern in any practical application.

Two-dimensional (2D) semi-Dirac systems, such as 2D black phosphorus and arsenene, can exhibit a rich topological phase transition between insulating, semi-Dirac, and band inversion phases when subjected to an external modulation. How these phase transitions manifest within the quantum transport and shot noise signatures remains an open question thus far. Here, we show that the Fano factor converges to the universal F ≈ 0.179 at the semi-Dirac phase and transits between the sub-Poissonian ( F ≈ 1 / 3) and the Poissonian shot noise ( F ≈ 1) limit at the band inversion and the insulating phase, respectively. Furthermore, the conductance of a 2D semi-Dirac system converges to the contrasting limit of G / G 0 → 1 / d and G / G 0 → 0 at the band inversion and the insulating phases, respectively. The quantum tunneling spectra exhibits a peculiar coexistence of massless and massive Dirac quasiparticles in the band inversion regime, thus providing a versatile sandbox to study the tunneling behavior of various Dirac quasiparticles. These findings reveal the rich interplay between band topology and quantum transport signatures, which may serve as smoking gun signatures for the experimental studies of semi-Dirac systems near the topological phase transition.

Using non-equilibrium Green's functions combined with many-body perturbation theory, we have calculated steady-state densities and currents through short interacting chains subject to a finite electric bias. By using a steady-state reverse-engineering procedure, the effective potential and bias which reproduce such densities and currents in a non-interacting system have been determined. The role of the effective bias is characterised with the aid of the so-called exchange-correlation bias, recently introduced in a steady-state density-functional- theory formulation for partitioned systems. We find that the effective bias (or, equivalently, the exchange-correlation bias) depends strongly on the interaction strength and the length of the central (chain) region. Moreover, it is rather sensitive to the level of many-body approximation used. Our study shows the importance of the effective/exchange-correlation bias out of equilibrium, thereby offering hints on how to improve the description of density- functional-theory based approaches to quantum transport.

A simplified quantum mechanical model is developed to investigate quantum transport features such as the electron concentration and the current flowing through a silicon nanowire metal-oxide-semiconductor field-effect transistor (MOSFET). In particular, the electron concentration is extracted from a self-consistent solution of the Schrödinger and Poisson equations as well as the ballistic Boltzmann equation which have been solved by exploiting a nonlinear variational principle within the framework of the generalized local density approximation. A suitable action functional has been minimized and details of the implementation and its numerical minimization are given. The current density and its related current-voltage characteristics are calculated from the one-dimensional ballistic steady-state Boltzmann transport equation which is solved analytically by using the method of characteristic curves. The straightforward implementation, the computational speed and the good qualitative behavior of the transport characteristics observed in our approach make it a promising simulation method for modeling quantum transport in nanowire MOSFETs.