Symmetry indicator in non-Hermitian systems

Abstract

Recently, topological phases in non-Hermitian systems have attracted much attention because non-Hermiticity sometimes gives rise to unique phases with no Hermitian counterparts. Non-Hermitian Bloch Hamiltonians can always be mapped to doubled Hermitianized Hamiltonians with chiral symmetry, which enables us to utilize the existing framework for Hermitian systems into the classification of non-Hermitian topological phases. While this strategy succeeded in the topological classification of non-Hermitian Bloch Hamiltonians in the presence of internal symmetries, the generalization of symmetry indicators -- a way to efficiently diagnose topological phases -- to non-Hermitian systems is still elusive. In this work, we study a theory of symmetry indicators for non-Hermitian systems. We define space group symmetries of non-Hermitian Bloch Hamiltonians as ones of the doubled Hermitianized Hamiltonians. Consequently, symmetry indicator groups for chiral symmetric Hermitian systems are equivalent to those for non-Hermitian systems. Based on this equivalence, we list symmetry indicator groups for non-Hermitian systems in the presence of space group symmetries. We also discuss the physical implications of symmetry indicators for some symmetry classes. Furthermore, explicit formulas of symmetry indicators for spinful electronic systems are included in appendices.

12+25 pages

References in corpus (17)

• Topological Crystalline Insulators
• Topological Origin of Non-Hermitian Skin Effects
• Topological Defects and Gapless Modes in Insulators and Superconductors
• The space group classification of topological band insulators
• Weyl Exceptional Rings in a Three-Dimensional Dissipative Cold Atomic Gas
• Topology of crystalline insulators and superconductors
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Double crystallographic groups and their representations on the Bilbao Crystallographic Server
• Magnetic Topological Quantum Chemistry
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topological Field Theory of Non-Hermitian Systems
• Topological classification and diagnosis in magnetically ordered electronic materials
• Non-Hermitian band topology with generalized inversion symmetry
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures

Cited by in corpus (23)

• Many-body topology of non-Hermitian systems
• Non-Hermitian Topological Phases: Principles and Prospects
• Dimerization induced mobility edges and multiple reentrant localization transitions in non-Hermitian quasicrystals
• Hermitian Bulk -- Non-Hermitian Boundary Correspondence
• Non-Hermitian higher-order topological superconductors in two-dimension: statics and dynamics
• Bulk-boundary correspondence in point-gap topological phases
• Universal platform of point-gap topological phases from topological materials
• Non-Hermitian spatial symmetries and their stabilized normal and exceptional topological semimetals
• Topological delocalization transitions and mobility edges in the nonreciprocal Maryland model
• Modified Generalized-Brillouin-Zone Theory with On-site Disorders
• Real Non-Hermitian Energy Spectra Without Any Symmetry
• Correlation-induced phase transitions and mobility edges in an interacting non-Hermitian quasicrystal
• Non-Hermitian skin effect enforced by nonsymmorphic symmetries
• Discriminant indicators with generalized inversion symmetry
• Nodal phases in non-Hermitian wallpaper crystals
• Discriminant indicator with generalized rotational symmetry
• Exceptional second-order topological insulators
• Two-body interaction induced phase transitions and intermediate phases in nonreciprocal non-Hermitian quasicrystals
• Non-Hermitian Hopf insulators
• Intrinsic non-Hermitian topological phases
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings
• Higher-order Topological Knots and the classification of non-Hermitian lattices under $C_n$ symmetry
• Anomalous Non-Hermitian Topological Anderson Insulator