Coherent transport in non-Abelian quantum graphs

TL;DR

This paper investigates quantum charge transport in 2D networks with magnetic and spin-orbit interactions, revealing complex conductance behaviors and classifying configurations with divergent localization corrections.

Contribution

It provides a classification of magnetic and spin-orbit field configurations affecting conductance and demonstrates a feasible setup for quantum graphs with non-Abelian gauge fields.

Findings

Conductance exhibits different periodicities in diffusive and ballistic regimes.

Certain configurations lead to logarithmically divergent weak localization corrections.

Conductivity varies between topologically distinct configurations in the ballistic regime.

Abstract

We study quantum charge transport in two-dimensional networks in the presence of a magnetic field and spin-orbit interaction. The interplay of the corresponding Abelian and non-Abelian gauge fields leads to an intricate behavior of the conductance, which has different periodicities in the diffusive and ballistic regimes. We classify all configurations of magnetic and spin-orbit fields where a logarithmically divergent weak-(anti)localization correction appears in the diffusive regime. The conductivity of topologically distinct configurations is the same in the diffusive regime but different in the ballistic regime. The proposed setup provides a feasible realization of quantum graphs with non-Abelian gauge fields.