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.
@article{arxiv.1805.08892,
title = {Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator},
author = {Timothy M. Philip and Mark R. Hirsbrunner and Matthew J. Gilbert},
journal= {arXiv preprint arXiv:1805.08892},
year = {2018}
}
Comments
7 pages, 3 figures. Supplement with 7 pages and 2 figures