Robust nonequilibrium surface currents in the three-dimensional Hofstadter model

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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 tunneling 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.
© The Author(s) 2022 M. T. M. is supported by a Royal Society-Science Foundation Ireland University Research Fellowship, and acknowledges funding from the ERC Starting Grant ODYSSEY (Grant Agreement No. 758403) and the Engineering and Physical Sciences Research Council-Science Foundation Ireland Joint Funding of Research project QuamNESS. A. R. and M. A. M.-D. acknowledge financial support from the Spanish MINECO grants MINECO/FEDER Projects No. FIS2017-91460-EXP, No. PGC2018-099169-B-I00FIS-2018 and from CAM/FEDER Project No. S2018/TCS-4342 (QUITEMAD-CM) . The research of A. R. and M. A. M.-D. has been partially supported by the U.S. Army Research Office through Grant No. W911NF-14-1-0103. Calculations were performed on the GICC cluster at UCM and the Lonsdale cluster maintained by the Trinity Centre for High Performance Computing, which was funded through grants from Science Foundation Ireland.
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