Signature of parity anomaly in the measurement of optical Hall conductivity in quantum anomalous Hall systems

TL;DR

This paper proposes an experimental scheme to detect the parity anomaly in quantum anomalous Hall systems by measuring nearly half-quantized optical Hall conductivity through Kerr, Faraday rotations, and absorption rates.

Contribution

It introduces a practical method to observe the parity anomaly via optical measurements in topological materials, highlighting frequency-dependent half-quantized Hall conductivity.

Findings

Optical Hall conductivity is nearly half-quantized in certain frequency ranges.

The behavior varies across different models, showing low and high-frequency regimes.

Measurement techniques include Kerr and Faraday rotations and circularly polarized light absorption.

Abstract

Parity anomaly is a quantum mechanical effect that the parity symmetry in a two-dimensional classical action is failed to be restored in any regularization of the full quantum theory and is characterized by a half-quantized Hall conductivity. Here we propose a scheme to explore the experimental signature from parity anomaly in the measurement of optical Hall conductivity, in which the optical Hall conductivity is nearly half quantized for a proper range of frequency. The behaviors of optical Hall conductivity are studied for several models, which reveal the appearance of half-quantized Hall conductivity in low or high-frequency regimes. The optical Hall conductivity can be extracted from the measurement of Kerr and Faraday rotations and the absorption rate of the circularly polarized light. This proposal provides a practical method to explore the signature of parity anomaly in topological quantum materials.