Kerr and Faraday rotations in topological flat and dispersive band structures

TL;DR

This paper investigates the dynamical Hall response in topological flat and dispersive bands, revealing the role of Van Hove singularities and demonstrating optical effects like Kerr and Faraday rotations linked to band topology.

Contribution

It identifies the Van Hove singularity as the key factor for sign changes in ac Hall conductivity and shows how flattening dispersive bands recovers flat band responses, guiding optical characterization.

Findings

Van Hove singularity causes sign change in $\sigma_{yx}(\omega)$

Flattening dispersive bands recovers IQH-like response

Topological bands exhibit giant Kerr and Faraday effects

Abstract

Integer quantum Hall (IQH) states and quantum anomalous Hall (QAH) states show the same static (dc) response but distinct dynamical (ac) response. In particular, the ac anomalous Hall conductivity profile $\sigma_{yx}(\omega)$ is sensitive to the band shape of QAH states. For example, dispersive QAH bands shows resonance profile without a sign change at the band gap while the IQH states shows the sign change resonance at the cyclotron energy. We argue by flattening the dispersive QAH bands, $\sigma_{yx}(\omega)$ should recover to that of flat Landau bands in IQH, thus it is necessary to know the origin of the sign change. Taking a topological lattice model with tunable bandwidth, we found that the origin of the sign change is not the band gap but the Van Hove singularity energy of the QAH bands. In the limit of small bandwidth, the flat QAH bands recovers $\sigma_{yx}(\omega)$ of the IQH Landau bands. Because of the Hall response, these topological bands exhibit giant polarization rotation and ellipticity in the reflected waves (Kerr effect) and rotation in the order of fine structure constant in the transmitted waves (Faraday effect) with profile resembles $\sigma_{yx}(\omega)$. Our results serve as a simple guide to optical characterization for topological flat bands.