Refined symmetry indicators for topological superconductors in all space groups

Abstract

Topological superconductors are exotic phases of matter featuring robust surface states that could be leveraged for topological quantum computation. A useful guiding principle for the search of topological superconductors is to relate the topological invariants with the behavior of the pairing order parameter on the normal-state Fermi surfaces. The existing formulas, however, become inadequate for the prediction of the recently proposed classes of topological crystalline superconductors. In this work, we advance the theory of symmetry indicators for topological (crystalline) superconductors to cover all space groups. Our main result is the exhaustive computation of the indicator groups for superconductors under a variety of symmetry settings. We further illustrate the power of this approach by analyzing four-fold symmetric superconductors with or without inversion symmetry, and show that the indicators can diagnose topological superconductors with surface states of different dimensionalities or dictate gaplessness in the bulk excitation spectrum.

arXiv comment14+38 pages; v2: discussions expanded, references updated

References in corpus (42)

• Topological insulators and superconductors
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Unpaired Majorana fermions in quantum wires
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological quantum chemistry
• Topological superconductors: a review
• The (High Quality) Topological Materials In The World
• Reflection symmetric second-order topological insulators and superconductors
• Catalogue of Topological Electronic Materials
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Odd-Parity Topological Superconductors: Theory and Application to Cu${}_x$Bi${}_2$Se${}_3$
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Towards ideal topological materials: Comprehensive database searches using symmetry indicators
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• The Challenge of Unconventional Superconductivity
• Fragile Topology and Wannier Obstructions
• Majorana Fermions and Topology in Superconductors
• Classification of topological insulators and superconductors in the presence of reflection symmetry
• Topology of Andreev Bound States with Flat Dispersion
• Quantitative mappings between symmetry and topology in solids
• Dirac and Weyl Superconductors in Three Dimensions
• Fermi Surface Topological Invariants for Time Reversal Invariant Superconductors
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Topological odd-parity superconductors
• Twisted equivariant matter
• Odd-parity topological superconductor with nematic order: Application to CuxBi2Se3
• Weak-Pairing Higher Order Topological Superconductors
• Topological phases protected by point group symmetry
• Building crystalline topological phases from lower-dimensional states
• Disconnected Elementary Band Representations, Fragile Topology, and Wilson Loops as Topological Indices: An Example on the Triangular Lattice
• Nematic superconductivity in doped Bi2Se3 topological superconductors
• Topological states from topological crystals
• Unified understanding of symmetry indicators for all internal symmetry classes
• Higher-Order Topological Superconductivity of Spin-Polarized Fermions
• Three-dimensional superconductors with hybrid higher order topology
• Atomic limit and inversion-symmetry indicators for topological superconductors
• Symmetry indicators for topological superconductors
• Fragile topological phases in interacting systems
• Pairing state at an interface of Sr${}_2$RuO${}_4$: parity-mixing, restored time-reversal symmetry, and topological superconductivity

Cited by in corpus (68)

• Spin-group symmetry in magnetic materials with negligible spin-orbit coupling
• Periodic Anderson model for magnetism and superconductivity in UTe2
• Superconductivity and Local Inversion-Symmetry Breaking
• Spin-Space Groups and Magnon Band Topology
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• Higher-order topological band structures
• Topological crystalline superconductivity in locally noncentrosymmetric CeRh${}_2$As${}_2$
• ${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups
• Two-dimensional Shiba lattices as possible platform for crystalline topological superconductivity
• Pairing Obstructions in Topological Superconductors
• 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
• High-throughput Investigations of Topological and Nodal Superconductors
• Topological Superconductivity in an s-wave Superconductor and Its Implication to Iron-based Superconductors
• Intrinsic first and higher-order topological superconductivity in a doped topological insulator
• Symmetry indicator in non-Hermitian systems
• Faithful derivation of symmetry indicators: A case study for topological superconductors with time-reversal and inversion symmetries
• Spin response and topology of a staggered Rashba superconductor
• Topological Crystalline Phases in a Disordered Inversion-Symmetric Chain
• Symmetry-based approach to nodal structures: Unification of compatibility relations and gapless point classifications
• Bulk-boundary-defect correspondence at disclinations in rotation-symmetric topological insulators and superconductors
• Euler Obstructed Cooper Pairing: Nodal Superconductivity and Hinge Majorana Zero Modes
• Coexistence of nontrivial topological properties and strong ferromagnetic fluctuations in $A_2$Cr${}_3$As${}_3$ ($A$=Na, K, Rb and Cs)
• Time-reversal-invariant $C_2$-symmetric higher-order topological superconductors
• Boundary Topological Superconductors
• Possible Realization of Topological Crystalline Superconductivity with Time-Reversal Symmetry in UTe2
• Topological Superconductivity from Unconventional Band Degeneracy with Conventional Pairing
• Higher-order topological superconductors from Weyl semimetals
• Theory of weak symmetry breaking of translations in ${\mathbb{Z}}_2$ topologically ordered states and its relation to topological superconductivity from an exact lattice ${\mathbb{Z}}_2$ charge-flux attachment
• Majorana multipole response: General theory and application to wallpaper groups
• Topological and nodal superconductor kagome magnesium triboride
• Optical $N$-insulators: topological obstructions in the atomistic susceptibility tensor
• Embedded Topological Semimetals
• Fragility of surface states in non-Wigner Dyson topological insulators
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Berry Phases of Vison Transport in ${\mathbb{Z}}_2$ Topologically Ordered States from Exact Fermion-Flux Lattice Dualities
• Chemical Principles of Intrinsic Topological Superconductors
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Higher-order topological and nodal superconducting transition-metal sulfides MS (M = Nb and Ta)
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Time-Reversal Symmetry and the Structure of Superconducting Order Parameter of Nearly Ferromagnetic Spin-Triplet Superconductor UTe2
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Topological superconductivity on the honeycomb lattice: Effect of normal state topology
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
• Direct demonstration of bulk-boundary correspondence in higher-order topological superconductors with chiral symmetry
• Topological gapless points in superconductors: From the viewpoint of symmetry
• All hourglass bosonic excitations in the 1651 magnetic space groups and 528 magnetic layer groups
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• MPd5 kagome superconductors studied by density functional calculations
• Higher-order topological superconductors characterized by Fermi level crossings
• $K$-theory classification of Wannier localizability and detachable topological boundary states
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Quasiparticle interference and spectral function of the UTe${}_2$ superconductive surface band
• Superconducting quantum criticality and the anomalous scaling: A nonlinear relativistic equation
• Fragile topology in nodal-line semimetal superconductors
• A proposal for realizing Majorana fermions without external magnetic field in strongly correlated nanowires
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Higher order topological state induced by $d$-wave competing orders in high-T${}_c$ superconductor based heterostructure
• Phase diagrams of superconducting topological surface states
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Frustration-free free fermions and beyond
• Theory of Topological Superconductivity in Doped IV-VI Semiconductors
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Inversion-symmetric Electron Gases as New Platforms for Topological Planar Josephson Junctions