Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator

TL;DR

This paper investigates how non-Hermitian effects in topological insulator heterostructures can lead to the loss of quantized Hall conductivity, challenging the robustness of topological invariants in open quantum systems.

Contribution

It demonstrates that non-Hermitian broadening from ferromagnetic coupling can obscure the quantized Hall effect in a topological insulator, revealing limitations of non-Hermitian topological classification.

Findings

Hall conductivity is no longer quantized in the non-Hermitian regime.

Non-Hermitian broadening can obscure the mass gap in spectral functions.

Experimental observation of QAHE in such heterostructures may be difficult.

Abstract

Recent work has extended topological band theory to open, non-Hermitian Hamiltonians, yet little is understood about how non-Hermiticity alters the topological quantization of associated observables. We address this problem by studying the quantum anomalous Hall effect (QAHE) generated in the Dirac surface states of a 3D time-reversal-invariant topological insulator (TI) that is proximity-coupled to a metallic ferromagnet. By constructing a contact self-energy for the ferromagnet, we show that in addition to generating a mass gap in the surface spectrum, the ferromagnet can introduce a non-Hermitian broadening term, which can obscure the mass gap in the spectral function. We calculate the Hall conductivity for the effective non-Hermitian Hamiltonian describing the heterostructure and show that it is no longer quantized despite being classified as a Chern insulator based on non-Hermitian topological band theory. Our results indicate that the QAHE will be challenging to experimentally observe in ferromagnet-TI heterostructures due to the finite lifetime of quasi-particles at the interface.