Robust nonequilibrium surface currents in the 3D Hofstadter model

TL;DR

This paper demonstrates the realization of robust, genuinely three-dimensional surface currents in a 3D Hofstadter model, revealing their stability against impurities, gauge tilting, and their dependence on discrete symmetries.

Contribution

It introduces a 3D lattice setup for Hofstadter model with robust surface currents, including boundary and crosscurrents, and explains their underlying symmetry-based mechanism.

Findings

Surface currents are stable against impurities and gauge tilting.

Protected boundary currents require tunneling in all three spatial directions.

Surface currents are robust for both bosonic and fermionic systems.

Abstract

Genuinely two-dimensional robust crosscurrents -- which flow against the natural direction of heat flux -- have been missing since the discovery of their one-dimensional counterpart. We provide a setup to realize them on a cubic three-dimensional (3D) lattice hosting a Hofstadter model coupled to two heat baths with different temperatures. We show that these currents exhibit dissipative robustness: they are stable against the presence of impurities and tilting of the gauge field in certain nonequilibrium configurations. Moreover, we find protected boundary currents with genuinely 3D robustness, i.e. they are only stable if tunnelling can occur in all three spatial directions. The model also presents generic surface currents, which are robust for both bosonic and fermionic systems. We identify the underlying qualitative mechanism responsible for the robustness of the surface currents and the crucial role played by certain discrete symmetries.