Unified understanding of symmetry indicators for all internal symmetry classes

Abstract

The interplay between symmetry and topology in electronic band structures has been one of the central subjects in condensed-matter physics. Recently, it has been getting clear that a wide variety of useful information about the band topology can be extracted by focusing the symmetry representations of valence bands without computing Wilson loops. In this work, we extend the previous studies on this subject to all 10 Altland-Zirnbauer symmetry classes in each of 230 space groups. We derive various general statements that should be useful in the search for topological superconductors and topological semimetals.

arXiv comment11 pages, 4 figures, 5 tables; v3: minor changes

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• Second-order topological non-Hermitian skin effects
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• Refined symmetry indicators for topological superconductors in all space groups
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Spectral signatures of the surface anomalous Hall effect in magnetic axion insulators
• Higher-Order Topological Dirac Superconductors
• Symmetry indicators of band topology
• Higher-order topological band structures
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Atomic limit and inversion-symmetry indicators for topological superconductors
• Topological classification and diagnosis in magnetically ordered electronic materials
• Temperature Dependent Electronic Structure in a Higher Order Topological Insulator Candidate EuIn${}_2$As${}_2$
• Non-Hermitian band topology with generalized inversion symmetry
• Multiple magnetic topological phases in bulk van der Waals crystal MnSb4Te7
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Symmetry indicators for topological superconductors
• Pfaffian formalism for higher-order topological insulators
• Chiral Hinge Magnons in Second-Order Topological Magnon Insulators
• Electronic structures and topological properties in nickelates $L{n}_{n+1}$Ni${}_n$O${}_{2n+2}$
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• Tenfold Topology of Crystals: Unified classification of crystalline topological insulators and superconductors
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Symmetry Indicators for Inversion-Symmetric Non-Hermitian Topological Band Structures
• Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators
• Symmetry indicator in non-Hermitian systems
• Faithful derivation of symmetry indicators: A case study for topological superconductors with time-reversal and inversion symmetries
• Symmetry-based approach to nodal structures: Unification of compatibility relations and gapless point classifications
• Euler Obstructed Cooper Pairing: Nodal Superconductivity and Hinge Majorana Zero Modes
• Appearance of hinge states in second-order topological insulators via the cutting procedure
• Theory of inversion-${\mathbb{Z}}_4$ protected topological chiral hinge states and its applications to layered antiferromagnets
• High-throughput screening for Weyl Semimetals with S${}_4$ Symmetry
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• The Bulk-Hinge Correspondence and Three-Dimensional Quantum Anomalous Hall Effect in Second Order Topological Insulators
• Intrinsically Interacting Higher-Order Topological Superconductors
• Variants of the symmetry-based indicator
• Two-dimensional weak-type topological insulators in inversion symmetric crystals
• Dynamic bulk-boundary correspondence for anomalous Floquet topology
• Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Topological insulators and higher-order topological insulators from gauge-invariant 1D lines
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Intrinsic ferromagnetic axion states and a single pair of Weyl fermions in the stable-state Mn\emph{X}${}_2$\emph{B}${}_2$\emph{T}${}_6$-family materials
• Rotoinversion-symmetric bulk-hinge correspondence and its applications to higher-order Weyl semimetals
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Discriminant indicators with generalized inversion symmetry
• Green's Function Approach to Interacting Higher-order Topological Insulators
• Intrinsic ferromagnetic and antiferromagnetic axion insulators in van der Waals materials Mn\emph{X}${}_2$\emph{B}${}_2$\emph{T}${}_6$ family
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
• Topological gapless points in superconductors: From the viewpoint of symmetry
• 5d orbital Induced Room Temperature Quantum Anomalous Hall Effect in TbCl
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• $Z_2$ Dirac points with topologically protected multihelicoid surface states
• Exceptional second-order topological insulators
• Discriminant indicator with generalized rotational symmetry
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Topological States in Chevrel Phase Materials from First-principle Calculations
• Mapping rules from nodal line semimetal to topological crystalline insulator in face centered cubic lattice
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Hybrid Higher-Order Skin Topological Modes in the Two-Dimensional Su-Schrieffer-Heeger Model with Nonreciprocal Hoppings