Topological flat Wannier-Stark bands

TL;DR

This paper investigates the spectral properties of a bipartite dice lattice under a dc bias, revealing flat bands with topological characteristics and localized eigenstates, advancing understanding of topological flat bands in driven quantum systems.

Contribution

It introduces a topological analysis of flat Wannier-Stark bands in a dice lattice under bias, highlighting the role of winding numbers and gap closings.

Findings

Flat energy bands form periodic multiplets with macroscopic degeneracy.

Eigenstates are exponentially localized perpendicular and super-exponentially along the bias.

Topological winding number (Zak phase) changes abruptly with bias, indicating topological phase transitions.

Abstract

We analyze the spectrum and eigenstates of a quantum particle in a bipartite two-dimensional tight-binding dice network with short range hopping under the action of a dc bias. We find that the energy spectrum consists of a periodic repetition of one-dimensional energy band multiplets, with one member in the multiplet being strictly flat. The corresponding macroscopic degeneracy invokes eigenstates localized exponentially perpendicular to the dc field direction, and super-exponentially along the dc field direction. We also show that the band multiplet is characterized by a topological winding number (Zak phase), which changes abruptly if we vary the dc field strength. These changes are induced by gap closings between the flat and dispersive bands, and reflect the number of these closings.