Time-dependent resonant tunneling transport: Keldysh and Kadanoff-Baym nonequilibrium Green's functions in an analytically soluble problem

TL;DR

This paper compares two nonequilibrium Green's function approaches for resonant tunneling structures, demonstrating their formal equivalence under certain conditions and providing explicit formulas for the lesser Green's function and current.

Contribution

It establishes the formal equivalence of the Keldysh and partition-free approaches in a wide-band, noninteracting limit, and derives explicit formulas for key transport quantities.

Findings

Both approaches are equivalent in the specified limit.

Explicit formulas for lesser Green's function and current are provided.

The study clarifies the relationship between two widely used methods.

Abstract

Here we address two nonequilibrium Green's functions approaches for a resonant tunneling structure under a sudden switch of a bias. Our aim is to stress that the time-dependent Keldysh formulation of Jauho, Wingreen and Meir, and the partition-free scheme of Stefanucci and Almbladh are formally equivalent in the ubiquitous case of wide-band limit and noninteracting electrons, if leads and dot are in equilibrium before the time-dependent perturbation. We develop explicit closed formulas of the lesser Green's function and time-dependent current, reminding that the different integration limits preclude a face-to-face comparison of two approaches. This study sheds light on both practices, which are of great interest to the mesoscopic transport community.