Transport in Conductors and Rectifiers: Mean-Field Redfield Equations and Non-Equilibrium Green's Functions

TL;DR

This paper develops a mean-field Redfield equation approach to quantum transport, deriving analytical steady-state solutions and validating results with non-equilibrium Green's function simulations, applicable to conductors and rectifiers.

Contribution

It introduces a closed-form equation of motion for quantum transport systems combining Redfield and mean-field methods, enabling analytical solutions and validation against established Green's function techniques.

Findings

Reproduces Landauer's formula for quantum wire conductance.

Demonstrates nonlinear rectification in semiconductor p-n junctions.

Shows good agreement with non-equilibrium Green's function simulations.

Abstract

We derive a closed equation of motion for the one particle density matrix of a quantum system coupled to multiple baths using the Redfield master equation combined with a mean-field approximation. The steady-state solution may be found analytically with perturbation theory. Application of the method to a one-dimensional non-interacting quantum wire yields an expression for the current that reproduces the celebrated Landauer's formula. Nonlinear rectification is found for the case of a mesoscopic three-dimensional semiconductor p-n junction. The results are in good agreement with numerical simulations obtained using non-equilibrium Green's functions, supporting the validity of the Redfield equations for the description of transport.