Kadanoff-Baym approach to quantum transport through interacting nanoscale systems: From the transient to the steady-state regime

TL;DR

This paper introduces a time-dependent many-body Green's function approach based on the Kadanoff-Baym equations to study the transient and steady-state electron dynamics in interacting nanoscale quantum transport systems, capturing correlations and external fields.

Contribution

It extends the Meir-Wingreen formula to the time domain and demonstrates the method's effectiveness through detailed simulations of a biased quantum wire with various many-body approximations.

Findings

Many-body effects significantly alter transient behavior and spectral features.

Second Born and GW approximations agree well for moderate interactions.

Interactions cause bias-dependent gap closing and quasiparticle broadening.

Abstract

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 level structure of the quantum wire out of equilibrium. For moderate interaction strenghts the 2B 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.