Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures

Abstract

We characterize non-Hermitian band structures by symmetry indicator topological invariants. Enabled by crystalline inversion symmetry, these indicators allow us to short-cut the calculation of conventional non-Hermitian topological invariants. In particular, we express the three-dimensional winding number of point-gapped non-Hermitian systems, which is defined as an integral over the whole Brillouin zone, in terms of symmetry eigenvalues at high-symmetry momenta. Furthermore, for time-reversal symmetric non-Hermitian topological insulators, we find that symmetry indicators characterize the associated Chern-Simons form, whose evaluation usually requires a computationally expensive choice of smooth gauge. In each case, we discuss the non-Hermitian surface states associated with nontrivial symmetry indicators.

6 pages, 1 figure, supplement included

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• Dislocation Non-Hermitian Skin Effect
• Non-Hermitian Topological Phases: Principles and Prospects
• Non-Hermitian band topology with generalized inversion symmetry
• Engineering Non-Hermitian Skin Effect with Band Topology in Ultracold Gases
• Hermitian Bulk -- Non-Hermitian Boundary Correspondence
• Theoretical Prediction of Non-Hermitian Skin Effect in Ultracold Atom Systems
• Bulk-boundary correspondence in point-gap topological phases
• Topology in non-Hermitian Chern insulators with skin effect
• Universal platform of point-gap topological phases from topological materials
• Symmetry indicator in non-Hermitian systems
• Non-Hermitian many-body topological excitations in interacting quantum dots
• Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals
• Topological phases of commensurate or incommensurate non-Hermitian Su-Schrieffer-Heeger lattices
• Infernal and Exceptional Edge Modes: Non-Hermitian Topology Beyond the Skin Effect
• Relationship between the Electronic Polarization and the Winding Number in Non-Hermitian Systems
• Discriminant indicators with generalized inversion symmetry
• Magnetic Flux Response of Non-Hermitian Topological Phases
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Lindbladian versus Postselected Non-Hermitian Topology
• Electronic polarization in non-Bloch band theory
• Discriminant indicator with generalized rotational symmetry
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings