Anomalous transport in a topological Wannier-Stark ladder

TL;DR

This paper investigates how a dc electric field in three-dimensional topological systems creates a ladder of Wannier-Stark bands with boundary states, leading to anomalous transport phenomena influenced by topological properties.

Contribution

It introduces the concept of topological Wannier-Stark ladders in 3D systems and analyzes their boundary states and transport properties under a dc field.

Findings

Boundary states fill energy gaps in the ladder.

Chiral boundary modes are tunable by field strength.

Anomalous transport persists due to topological boundary states.

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.