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arXiv · 1805.08892

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

Timothy M. Philip·Mark R. Hirsbrunner·Matthew J. Gilbert
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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.

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Timothy M. Philip, Mark R. Hirsbrunner, Matthew J. Gilbert. 2018-05-22. Loss of Hall Conductivity Quantization in a Non-Hermitian Quantum Anomalous Hall Insulator. https://doi.org/10.1103/physrevb.98.155430

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