Weak localization in multiterminal networks of diffusive wires

TL;DR

This paper investigates quantum transport in networks of diffusive wires, revealing how weak localization corrections depend on network geometry and introducing a new effect that can reverse the correction's sign.

Contribution

It introduces a method to compute weak localization corrections in arbitrary wire networks, emphasizing the importance of proper cooperon weighting and nonlocal effects.

Findings

Derived conductance matrix using diagrammatic method

Identified how network geometry affects weak localization corrections

Predicted a new geometrical effect that can change the sign of the correction

Abstract

We study the quantum transport through networks of diffusive wires connected to reservoirs in the Landauer-B\"uttiker formalism. The elements of the conductance matrix are computed by the diagrammatic method. We recover the combination of classical resistances and obtain the weak localization corrections. For arbitrary networks, we show how the cooperon must be properly weighted over the different wires. Its nonlocality is clearly analyzed. We predict a new geometrical effect that may change the sign of the weak localization correction in multiterminal geometries.