Scattering matrix approach to interacting electron transport

TL;DR

This paper uses a scattering matrix approach to analyze how electron-electron interactions modify mesoscopic electronic transport, revealing that interactions can be incorporated via renormalized transmission in linear response but require additional considerations beyond that.

Contribution

It demonstrates that scattering matrices can be used to incorporate interaction effects in mesoscopic transport, including beyond linear response and spin-dependent correlations.

Findings

Interaction effects can be included through renormalized transmission in linear response.

Beyond linear response, additional two-particle processes affect current correlations.

Interaction enhances opposite-spin current correlations in asymmetric scatterers.

Abstract

We investigate the modification in mesoscopic electronic transport due to electron-electron interactions making use of scattering states. We demonstrate that for a specific (finite range) interaction kernel, the knowledge of the scattering matrix is sufficient to take interaction effects into account. We calculate perturbatively the corrections to the current and current-current correlator; in agreement with previous work, we find that, in linear response, interaction effects can be accounted for by an effective (renormalized) transmission probability. Beyond linear response, simple renormalization of scattering coefficients is not sufficient to describe the current-current correlator, as additional corrections arise due to irreducible two-particle processes. Furthermore, we find that the correlations between opposite-spin currents induced by interaction are enhanced for an asymmetric scatterer, generating a nonzero result already to lowest order in the interaction.