We study a system of two non-interacting quantum wires with fermions of opposite chirality with a point-contact junction at the origin across which tunneling can take place when an arbitrary time-dependent bias between the wires is applied. We obtain the exact dynamical non-equilibrium Green function by solving Dyson's equation analytically. Both the space-time dependent two and four-point functions are written down in a closed form in term of simple functions of position and time. This allows us to obtain among other things, the I-V characteristics for an arbitrary time-dependent bias. Our method is a superior alternative to competing approaches to non-equilibrium as we are able to account for transient phenomena as well as the steady state. We study the approach to steady state by computing the time-evolution of the equal-time one-particle Green function. We also show how the presence of the point-contact affects the density profile of the electrons by inducing Friedel oscillations in the system and how the presence of a bias influences these oscillations.
We study a system of two non-interacting quantum wires with fermions of opposite chirality with a point-contact junction at the origin across which tunneling can take place when an arbitrary time-dependent bias between the wires is applied. We obtain the exact dynamical non-equilibrium Green function by solving Dyson's equation analytically. Both the space-time dependent two and four-point functions are written down in a closed form in term of simple functions of position and time. This allows us to obtain among other things, the I-V characteristics for an arbitrary time-dependent bias. Our method is a superior alternative to competing approaches to non-equilibrium as we are able to account for transient phenomena as well as the steady state. We study the approach to steady state by computing the time-evolution of the equal-time one-particle Green function. We also show how the presence of the point-contact affects the density profile of the electrons by inducing Friedel oscillations in the system and how the presence of a bias influences these oscillations.
Abstract We study a system of two non-interacting quantum wires with fermions of opposite chirality with a point contact junction at the origin across which tunneling can take place when an arbitrary time-dependent bias between the wires is applied. We obtain the exact dynamical non-equilibrium Green function by solving Dyson’s equation analytically. Both the space–time dependent two and four-point functions are written down in a closed form in terms of simple functions of position and time. This allows us to obtain, among other things, the I–V characteristics for an arbitrary time-dependent bias. Our method is a superior alternative to competing approaches to non-equilibrium as we are able to account for transient phenomena as well as the steady state. We study the approach to steady state by computing the time evolution of the equal-time one-particle Green function. Our method can be easily applied to the problem of a double barrier contact whose internal properties can be adjusted to induce resonant tunneling leading to a conductance maximum. We then consider the case of a finite bandwidth in the point contact and calculate the non-equilibrium transport properties which exhibit non-Markovian behaviour. When a subsequently constant bias is suddenly switched on, the current shows a transient build up before approaching its steady state value in contrast to the infinite bandwidth case. This transient property is consistent with numerical simulations of lattice systems using time-dependent density matrix renormalization group suggesting thereby that this transient build up is merely due to the presence of a short distance cutoff in the problem description and not on the other details.
Non-chiral bosonization technique adapted to study chiral quantum wires with non-interacting fermions coupled through a point-contact with a constant bias between the wires is introduced and is shown to reproduce the exact Green functions of this system which was previously derived by the present authors analytically using standard methods. The tunneling I-V characteristics are obtained using the bosonized Green functions. The proposed unconventional bosonization scheme is also shown to be internally consistent as the four-point functions evaluated using NCBT are shown to be related to the two-point functions through Wick's theorem as it should be. In equilibrium, the equal space-time NCBT Green functions for an interacting Luttinger liquid with impurities obtained in a previous work shows universal scaling behaviour in accordance with Bethe ansatz and functional renormalization group predictions. We expect to obtain a similar scaling form of the tunneling properties out of equilibrium in presence of interparticle interactions.
We propose a time-dependent many-body approach to study the short-time dynamics of correlated electrons in quantum transport through nanoscale systems contacted to metallic leads. This approach is based on the time propagation of the Kadanoff-Baym equations for the nonequilibrium many-body Green's function of open and interacting systems out of equilibrium. An important feature of the method is that it takes full account of electronic correlations and embedding effects in the presence of time-dependent external fields, while at the same time satisfying the charge conservation law. The method further extends the Meir-Wingreen formula to the time domain for initially correlated states. We study the electron dynamics of a correlated quantum wire attached to two-dimensional leads exposed to a sudden switch on of a bias voltage using conserving many-body approximations at Hartree-Fock, second Born and GW level. We obtain detailed results for the transient currents, dipole moments, spectral functions, charging times, and the many-body screening of the quantum wire as well as for the time-dependent density pattern in the leads, and we show how the time dependence of these observables provides a wealth of information on the energy level structure of the quantum wire out of equilibrium. For moderate interaction strengths the second Born and GW results are in excellent agreement at all times. We find that many-body effects beyond the Hartree-Fock approximation have a large effect on the qualitative behavior of the system and lead to a bias-dependent gap closing and quasiparticle broadening, shortening of the transient times and washing out of the step features in the current-voltage curves.
In this thesis the electron transport through interacting quantum wires is studied.The time-dependent properties of the system are investigated by using the non-equilibrium Green function technique.This technique provides a way to include ultra-fast timedependent processes, arbitrary strong external fields and also brings forward an effective treatment of electron-electron and electron-phonon interactions.The electronelectron interactions are included via various self-energy approximations at Hartree-Fock, second-order Born and GW levels.These approximations are called conserving since they fulfill the physical conservation laws like the charge conservation law.The interacting central system is coupled to one-dimensional tight-binding leads, which are considered effectively as noninteracting.The system is perturbed by a bias voltage after which the time-evolution of the system is followed by Kadanoff-Baym equations.The non-equilibrium steady-state value of the current depends on the used self-energy approximation, which indicates the importance of the history-dependence in the calculation of current.This is an important observation in the aspect of time-dependent density functional theory, since it is one indication for the need of functionals with memory.The steady-state current is independent of the initial state, which is in accordance with the memory-loss theorem.The transient current shows small oscillations, which are consequence of the density oscillations especially in the first and last site.The density oscillations in the sites are effect of the electron transition from the lead to the central system and vice versa.
We consider electron transport in a model of a spinless superconductor described by a Kitaev-type lattice Hamiltonian where the electron interactions are modeled through a superconducting pairing term. The superconductor is sandwiched between two normal metals that are kept at different temperatures and chemical potentials and that are themselves modeled as noninteracting spinless fermions. For this setup we compute the exact steady-state properties of the system using the quantum-Langevin-equation approach. Closed-form exact expressions for particle current, energy current, and other two-point correlations are obtained in the Landauer-type forms and involve two nonequilibrium Green's functions. The current expressions are found to be the sum of three terms having simple physical interpretations. We then discuss a numerical approach where we construct the time evolution of the two-point correlators of the system from the eigenspectrum of the complete quadratic Hamiltonian describing the system and leads. By starting from an initial state corresponding to the leads in thermal equilibrium and the system in an arbitrary state, the long-time solution for the correlations, before recurrence times, gives us steady-state properties. We use this independent numerical method for verifying the results of the exact solution. We also investigate analytically the presence of high-energy bound states and obtain expressions for their contributions to two-point correlators. As applications of our general formalism we present results on thermal conductance and on the conductance of a Kitaev chain with next-nearest-neighbor interactions which allows topological phases with different winding numbers.
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.