$G_Q$-corrections in Circuit Theory of Quantum Transport

TL;DR

This paper introduces a finite-element method to evaluate $G_Q$-order corrections in quantum transport, applicable to various properties of nanostructures, including conductance, noise, and superconducting features.

Contribution

The authors develop a versatile finite-element technique based on Green functions to compute $G_Q$-corrections for diverse transport phenomena in nanostructures.

Findings

Method successfully applied to transitions between ensembles.

Analyzed Aharonov-Bohm effect within the framework.

Extended the approach to non-equilibrium transport and fluctuations.

Abstract

We develop a finite-element technique that allows one to evaluate correction of the order of $G_Q$ to various transport characteristics of arbitrary nanostructures. Common examples of such corrections are weak localization effect on conductance and universal conductance fluctuations. Our approach, however, is not restricted to conductance only. It allows in the same manner to evaluate corrections to noise characteristics, superconducting properties, strongly non-equilibrium transport and transmission distribution. To enable such functionality, we consider Green functions of arbitrary matrix structure. We derive a finite-element technique from Cooperon and Diffuson ladders for these Green's functions. The derivation is supplemented with application examples. Those include transitions between ensembles and Aharonov-Bohm effect.