Electron transport in a one dimensional conductor with inelastic scattering by self-consistent reservoirs

TL;DR

This paper extends a model of electron transport in one-dimensional conductors by incorporating finite temperature effects and inelastic scattering via self-consistent reservoirs, providing exact solutions for transport coefficients and analyzing heat dissipation patterns.

Contribution

It introduces an exact solution for electron and heat transport in a 1D conductor with inelastic scattering at finite temperatures using quantum Langevin equations and Green's functions.

Findings

Dissipation is uniform along long wires with inelastic scattering.

Ballistic transport shows dissipation mainly at contacts.

Chemical potential profile is linear with boundary jumps in intermediate regimes.

Abstract

We present an extension of the work of D'Amato and Pastawski on electron transport in a one-dimensional conductor modeled by the tight binding lattice Hamiltonian and in which inelastic scattering is incorporated by connecting each site of the lattice to one-dimensional leads. This model incorporates B\"uttiker's original idea of dephasing probes. Here we consider finite temperatures and study both electrical and heat transport across a chain with applied chemical potential and temperature gradients. Our approach involves quantum Langevin equations and nonequilibrium Green's functions. In the linear response limit we are able to solve the model exactly and obtain expressions for various transport coefficients. Standard linear response relations are shown to be valid. We also explicitly compute the heat dissipation and show that for wires of length $N >> \ell$, where $\ell$ is a coherence length scale, dissipation takes place uniformly along the wire. For $N << \ell$, when transport is ballistic, dissipation is mostly at the contacts. In the intermediate range between Ohmic and ballistic transport we find that the chemical potential profile is linear in the bulk with sharp jumps at the boundaries. These are explained using a simple model where the left and right moving electrons behave as persistent random walkers.