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

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.

arXiv comment7 pages, 3 figures. Supplement with 7 pages and 2 figures

References in corpus (21)

• Topological Insulators
• Topological insulators and superconductors
• Anomalous Hall effect
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Quantized Anomalous Hall Effect in Magnetic Topological Insulators
• Topological Band Theory for Non-Hermitian Hamiltonians
• Non-Hermitian Chern bands
• Observation of Bulk Fermi Arc and Polarization Half Charge from Paired Exceptional Points
• Scale-Invariant Dissipationless Chiral Transport in Magnetic Topological Insulators beyond the Two-Dimensional Limit
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Theory of the topological Anderson insulator
• Precise quantization of anomalous Hall effect near zero magnetic field
• Anomalous Hall effect in 2D Dirac band: link between Kubo-Streda formula and semiclassical Boltzmann equation approach
• Emergent quantum confinement at topological insulator surfaces
• Majorana bound states from exceptional points in non-topological superconductors
• Flat Band in Disorder Driven Non-Hermitian Weyl Semimetals
• Weak Localization and Antilocalization in Topological Insulator Thin Films with Coherent Bulk-Surface Coupling
• Massive Dirac surface states in topological insulator/magnetic insulator heterostructures
• Effects of non-Hermitian perturbations on Weyl Hamiltonians with arbitrary topological charges
• Part-per-million quantization and current-induced breakdown of the quantum anomalous Hall effect
• Anomalous Hall effect in a two-dimensional electron gas

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