${\mathbb{Z}}_2$-enriched symmetry indicators for topological superconductors in the 1651 magnetic space groups

Abstract

While the symmetry-based diagnosis of topological insulators and semimetals has enabled large-scale discovery of topological materials candidates, the extension of these approaches to the diagnosis of topological superconductors remains a major open question. One important new ingredient in the analysis of topological superconductivity is the presence of ${\mathbb{Z}}_2$-valued Pfaffian invariants associated with certain high-symmetry momenta. Such topological invariants lie beyond the conventional scope of symmetry representation theory for band structures, and as such they are nontrivial to incorporate into the systematic calculations of the symmetry indicators of band topology. Here, we overcome this challenge and report the full computation of the ${\mathbb{Z}}_2$-enriched symmetry indicators for superconductors in all symmetry settings. Our results indicate that incorporating the ${\mathbb{Z}}_2$ band labels enhance the diagnostic power of the scheme in roughly $60\%$ of the symmetry settings. Our framework can also be readily integrated with first-principles calculations to elucidate on the possible properties of unconventional superconductivity in a given compound. As a demonstration, we analyze explicitly the interplay between pairing symmetry and topological superconductivity in the recently discovered superconductors CaPtAs and CaSb${}_2$.

arXiv comment(6 + 171) pages

References in corpus (62)

• Quantum ESPRESSO: a modular and open-source software project for quantum simulations of materials
• Advanced capabilities for materials modelling with Quantum ESPRESSO
• Non-Abelian Anyons and Topological Quantum Computation
• Weyl and Dirac Semimetals in Three Dimensional Solids
• Topological Insulators with Inversion Symmetry
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Topological Crystalline Insulators in the SnTe Material Class
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• The (High Quality) Topological Materials In The World
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Experimental realization of a topological crystalline insulator in SnTe
• 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 classification of crystalline insulators through band structure combinatorics
• Inversion Symmetric Topological Insulators
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Majorana Fermions and Topology in Superconductors
• Quantitative mappings between symmetry and topology in solids
• Dirac and Weyl Superconductors in Three Dimensions
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Fermi Surface Topological Invariants for Time Reversal Invariant Superconductors
• Symmetry indicators and anomalous surface states of topological crystalline insulators
• Quantized Response and Topology of Insulators with Inversion Symmetry
• Topological odd-parity superconductors
• Bogoliubov Fermi surfaces in superconductors with broken time-reversal symmetry
• Robust doubly charged nodal lines and nodal surfaces in centrosymmetric systems
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Gauging spatial symmetries and the classification of topological crystalline phases
• Rotation Anomaly and Topological Crystalline Insulators
• Topological Blount's theorem of odd-parity superconductors
• Connecting higher-order topological insulators to lower-dimensional topological insulators
• Refined symmetry indicators for topological superconductors in all space groups
• Topological states from topological crystals
• Unified understanding of symmetry indicators for all internal symmetry classes
• Crystalline topological phases as defect networks
• Higher-Order Topological Superconductivity of Spin-Polarized Fermions
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Simultaneous Nodal Superconductivity and Time-Reversal Symmetry Breaking in the Noncentrosymmetric Superconductor CaPtAs
• Symmetry indicators of band topology
• Classification of Crystalline Topological Insulators and Superconductors with Point Group Symmetries
• Topological Materials Discovery By Large-order symmetry indicators
• Atomic limit and inversion-symmetry indicators for topological superconductors
• Unconventional superconducting gap structure protected by space group symmetry
• 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
• Classification of topological crystalline superconducting nodes on high-symmetry lines: Point nodes, line nodes, and Bogoliubov Fermi surfaces
• Möbius topological superconductivity in UPt${}_3$
• Pfaffian formalism for higher-order topological insulators
• $Z_4$ Topological Superconductivity in UCoGe
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• Faithful derivation of symmetry indicators: A case study for topological superconductors with time-reversal and inversion symmetries
• Superconductivity in the nonsymmorphic line-nodal compound CaSb${}_2$

Cited by in corpus (44)

• Spin-group symmetry in magnetic materials with negligible spin-orbit coupling
• Spin-Space Groups and Magnon Band Topology
• Topological crystalline superconductivity in locally noncentrosymmetric CeRh${}_2$As${}_2$
• Real-space construction of crystalline topological superconductors and insulators in 2D interacting fermionic systems
• High-throughput Investigations of Topological and Nodal Superconductors
• Intrinsic first and higher-order topological superconductivity in a doped topological insulator
• Symmetry indicator in non-Hermitian systems
• Spin response and topology of a staggered Rashba superconductor
• $N$-band Hopf insulator
• 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
• Topological Superconductivity from Unconventional Band Degeneracy with Conventional Pairing
• Possible Realization of Topological Crystalline Superconductivity with Time-Reversal Symmetry in UTe2
• MSGCorep: A package for corepresentations of magnetic space groups
• Intrinsically Interacting Higher-Order Topological Superconductors
• 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
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Topological and nodal superconductor kagome magnesium triboride
• Embedded Topological Semimetals
• Higher-order topological semimetals and nodal superconductors with an order-two crystalline symmetry
• Strongly correlated crystalline higher-order topological phases in two-dimensional systems: A coupled-wire study
• Higher-order topological and nodal superconducting transition-metal sulfides MS (M = Nb and Ta)
• Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe${}_2$
• Generalized Fermion Doubling Theorems: Classification of 2D Nodal Systems in Terms of Wallpaper Groups
• Peak in the superconducting transition temperature of the nonmagnetic topological line-nodal material CaSb${}_2$ under pressure
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Superconductivity and Quantum Oscillations in Single Crystals of the Compensated Semimetal CaSb${}_2$
• Quasi-2D Fermi surface of superconducting line-nodal metal CaSb${}_2$
• Nodeless superconductivity in the topological nodal-line semimetal CaSb2
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Classification of time-reversal symmetric topological superconducting phases for conventional pairing symmetries
• 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
• Fermiology of a topological line-nodal compound CaSb2 and its implication to superconductivity: angle-resolved photoemission study
• Atiyah-Hirzebruch spectral sequence for topological insulators and superconductors: $E_2$ pages for 1651 magnetic space groups
• Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems
• Pressure evolution of the normal- and superconducting-state properties of the line-nodal material CaSb${}_2$ revealed by ${}^{123}$Sb nuclear quadrupole resonance
• Hinge Majorana Flat Band in Type-II Dirac Semimetals
• Global and Local Topological Crystalline Markers for Rotation-Symmetric Insulators
• Superconducting Gap Structures in Wallpaper Fermion Systems
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals
• Weak ${\mathbb{Z}}_2$ Supertopology