A nonequilibrium theory for transient transport dynamics in nanostructures via the Feynman-Vernon influence functional approach

TL;DR

This paper develops an exact nonequilibrium theory for transient electron transport in nanostructures, capturing non-Markovian effects and non-linear responses, extending previous models to time-dependent systems with detailed analytical and numerical results.

Contribution

It introduces a nonperturbative, exact framework for transient quantum transport in nanostructures with time-dependent parameters, including back-reaction effects and non-Markovian dynamics.

Findings

Demonstrates non-Markovian memory effects in transient transport

Provides analytical solutions for resonance tunneling devices

Shows non-linear response to ac bias voltages

Abstract

In this paper, we develop a nonequilibrium theory for transient electron transport dynamics in nanostructures based on the Feynman-Vernon influence functional approach. We extend our previous work on the exact master equation describing the non-Markovian electron dynamics in the double dot [Phys. Rev. B78, 235311 (2008)] to the nanostructures in which the energy levels of the central region, the couplings to the leads and the external biases applied to leads are all time-dependent. We then derive nonperturbatively the exact transient current in terms of the reduced density matrix within the same framework. This provides an exact non-linear response theory for quantum transport processes with back-reaction effect from the contacts, including the non-Markovian quantum relaxation and dephasing, being fully taken into account. The nonequilibrium steady-state transport theory based on the Schwinger-Keldysh nonequilibrium Green function technique can be recovered as a long time limit. For a simple application, we present the analytical and numerical results of transient dynamics for the resonance tunneling nanoscale device with a Lorentzian-type spectral density and ac bias voltages, where the non-Markovian memory structure and non-linear response to the bias voltages in transport processes are demonstrated.