Four-terminal resistances in mesoscopic networks of metallic wires: Weak localisation and correlations

TL;DR

This paper investigates weak localisation effects and resistance correlations in mesoscopic metallic wire networks, providing a formalism to understand how quantum interference influences four-terminal resistances and their fluctuations.

Contribution

It introduces a new formalism linking weak localisation corrections and resistance correlations to classical transport properties in mesoscopic networks.

Findings

Weak localisation can significantly alter four-terminal resistances.

The same weights used for WL corrections apply to resistance correlations.

Formalism is demonstrated on multiconnected wire geometries.

Abstract

We consider the electronic transport in multi-terminal mesoscopic networks of weakly disordered metallic wires. After a brief description of the classical transport, we analyze the weak localisation (WL) correction to the four-terminal resistances, which involves an integration of the Cooperon over the wires with proper weights. We provide an interpretation of these weights in terms of classical transport properties. We illustrate the formalism on examples and show that weak localisation to four-terminal conductances may become large in some situations. In a second part, we study the correlations of four-terminal resistances and show that integration of Diffuson and Cooperon inside the network involves the same weights as the WL. The formulae are applied to multiconnected wire geometries.