Replacing Leads by Self-Energies Using Nonequilibrium Green's Functions

TL;DR

This paper explores how leads in open quantum systems can be replaced by self-energies within the nonequilibrium Green's function framework, simplifying transport calculations while analyzing the dependence on unperturbed Green's functions.

Contribution

It demonstrates the flexibility in choosing unperturbed Green's functions and shows that leads can be replaced by energy-dependent self-energies, simplifying nonequilibrium transport analysis.

Findings

Retarded self-energy depends on the choice of unperturbed Green's function.

Nonequilibrium self-energy can be independent of this choice.

Transport calculations become simpler when expressed in terms of self-energies.

Abstract

An open quantum system consists of leads connected to a device of interest. Within the nonequilibrium Green's function technique, we examine the replacement of leads by self-energies in continuum calculations. Our starting point is a formulation of the problem for continuum systems by T.E. Feuchtwang. In this approach there is considerable flexibility in the choice of unperturbed Green's functions. We examine the consequences of this freedom on the treatment of leads. For any choice the leads can be replaced by coupling self-energies which are simple functions of energy. We find that the retarded self-energy depends on the details of the choice of unperturbed Green's function, and can take any value. However, the nonequilibrum self-energy or scattering function can be taken to be independent of this choice. Expressed in terms of these self-energies, nonequilibrium transport calculations take a particularly simple form.