Real space topological invariant and higher-order topological Anderson insulator in two-dimensional non-Hermitian systems

Abstract

We study the characterization and realization of higher-order topological Anderson insulator (HOTAI) in non-Hermitian systems, where the non-Hermitian mechanism ensures extra symmetries as well as gain and loss disorder.We illuminate that the quadrupole moment $Q_{xy}$ can be used as the real space topological invariant of non-Hermitian higher-order topological insulator (HOTI). Based on the biorthogonal bases and non-Hermitian symmetries, we prove that $Q_{xy}$ can be quantized to $0$ or $0.5$. Considering the disorder effect, we find the disorder-induced phase transition from normal insulator to non-Hermitian HOTAI. Furthermore, we elucidate that the real space topological invariant $Q_{xy}$ is also applicable for systems with the non-Hermitian skin effect. Our work enlightens the study of the combination of disorder and non-Hermitian HOTI.

9 pages,6 figures

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• Bulk-boundary correspondence in point-gap topological phases
• Topological Anderson insulators induced by random binary disorders
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Topological Anderson amorphous insulator
• Universal non-Hermitian transport in disordered systems
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Real Non-Hermitian Energy Spectra Without Any Symmetry
• Engineering topologically protected zero-dimensional interface end states in antiferromagnetic heterojunction graphene nanoflakes
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• Anatomy of topological Anderson transitions
• Quantized charge-pumping in higher-order topological insulators
• Observation of disorder-induced boundary localization
• Topological quantum transition driven by charge-phonon coupling in higher-order topological insulators
• Hermitian chiral boundary states in non-Hermitian topological insulators
• Corner modes in non-Hermitian next-nearest-neighbor hopping model
• Berezinskii-Kosterlitz-Thouless localization-localization transitions in disordered two-dimensional quantized quadrupole insulators
• Higher-order topology in twisted multilayer systems: a review
• Unifying Anderson transitions and topological amplification in non-Hermitian chains
• Recent progress on disorder-induced topological phases
• Disorder-induced chiral and helical Majorana edge modes in a two-dimensional Ammann-Beenker quasicrystal
• Non-Hermitian second-order topological insulator with point gap
• Anomalous Non-Hermitian Topological Anderson Insulator