Abstract
A dc (e.g. electric) field with commensurate lattice direction turns a single particle band structure in $d=3$ dimensions into an infinite set of equally spaced irreducible $(d-1)=2$-dimensional Wannier-Stark (WS) band structures that are spatially localized along the field direction. Particle transport is expected to be suppressed once the WS bands are gapped in energy. The topological character of the irreducible band structure leads to one-dimensional sets of boundary states which fill the energy gaps. As a result, eigenmodes are smoothly connected in energy and space and yield anomalous particle transport throughout the ladder. The number of chiral boundary modes can be tuned by the dc field strength and manifests through the distribution of dissipated energy and spatial motion, and the temperature dependence of angular momentum carried by particles.
Highlights
Particle transport in quantum mechanical systems is of fundamental interest in condensed matter physics
The above cases demonstrate that the number of 1D edge/boundary modes localized at the open boundary at E = 0 and E = ±F/2 are tuned by the external electric field strength
We theoretically study topological phases of a 3D WS ladder, which shares the same topological property with Floquet topological phases in (2 + 1) dimensions
Summary
Particle transport in quantum mechanical systems is of fundamental interest in condensed matter physics. We present a study of edge particle and thermal transport along the dc electric field direction of a WS ladder with a nontrivial topological character in d = 3 space dimensions. As opposed to in-gap impurity states for which spatially localized modes have random energies and spatial locations, the topological protection of boundary states ensures continuous distribution of eigenmodes in energy space with a finite spatial overlap among neighboring modes This provides a weak but robust transport of particles across the energy gap regardless of the cutoff energy of heat bath, which otherwise will show transport properties similar to insulators
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