Atomic limit and inversion-symmetry indicators for topological superconductors

Abstract

Symmetry indicators have proven to be extremely helpful in identifying topologically non-trivial crystalline insulators using symmetry-group representations of their Bloch states. An extension of this approach to superconducting systems requires defining an appropriate atomic limit for Bogoliubov-de-Gennes Hamiltonians. Here, we introduce such a notion of atomic limit and derive a ${\mathbb{Z}}_{2^d}$-valued symmetry indicator for inversion-symmetric superconductors of $d$ dimensions. This indicator allows for a refined topological classification including higher-order phases for systems in the superconducting symmetry classes D and DIII. We further elucidate the bulk-boundary correspondence of these phases using Dirac surface theories. Requiring only the normal-state band structure and the superconducting order-parameter symmetry as an input, this indicator is well suited for a search of topological superconductors using first-principles calculations.

arXiv comment5 pages, 1 figure, 2 tables

References in corpus (32)

• Unpaired Majorana fermions in quantum wires
• Topological Insulators in Three Dimensions
• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Quantized Electric Multipole Insulators
• Non-abelian statistics of half-quantum vortices in p-wave superconductors
• Higher-Order Topological Insulators
• 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
• 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
• Topological classification of crystalline insulators through band structure combinatorics
• Spontaneously polarized half-gapped superconductivity
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• 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
• Topological odd-parity superconductors
• Weyl superconductors
• Efficient Topological Materials Discovery Using Symmetry Indicators
• Weak-Pairing Higher Order Topological Superconductors
• Chiral $d$-wave Superconductivity in SrPtAs
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Unified understanding of symmetry indicators for all internal symmetry classes
• Superconductivity in Uranium Ferromagnets
• Symmetry indicators for topological superconductors
• Classification of topological crystalline superconducting nodes on high-symmetry lines: Point nodes, line nodes, and Bogoliubov Fermi surfaces

Cited by in corpus (46)

• Inversion-protected higher order topological superconductivity in monolayer WTe${}_2$
• Refined symmetry indicators for topological superconductors in all space groups
• Periodic Anderson model for magnetism and superconductivity in UTe2
• Topological and holonomic quantum computation based on second-order topological superconductors
• Superconductivity and Local Inversion-Symmetry Breaking
• Higher-Order Topological Superconductivity of Spin-Polarized Fermions
• Symmetry-based indicators for topological Bogoliubov-de Gennes Hamiltonians
• Higher-Order Topological Dirac Superconductors
• Chiral Dirac Superconductors: Second-order and Boundary-obstructed Topology
• All-electrically tunable networks of Majorana bound states
• Symmetry indicators of band 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
• WannSymm: A symmetry analysis code for Wannier orbitals
• Pairing Obstructions in Topological Superconductors
• qeirreps: an open-source program for Quantum ESPRESSO to compute irreducible representations of Bloch wavefunctions
• High-throughput Investigations of Topological and Nodal Superconductors
• Symmetry indicator in non-Hermitian systems
• Spin response and topology of a staggered Rashba superconductor
• 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
• Superconductors with anomalous Floquet higher-order topology
• Time-reversal-invariant $C_2$-symmetric higher-order topological superconductors
• Non-perturbative constraints from symmetry and chirality on Majorana zero modes and defect quantum numbers in (2+1)D
• Nodal higher-order topological superconductivity from a ${\mathcal{C}}_4$-symmetric Dirac semimetal
• Higher-order topological superconductors from Weyl semimetals
• Majorana multipole response: General theory and application to wallpaper groups
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Magnetic Response of Majorana Kramers Pairs Protected by Z2 Invariants
• Thermodynamic transitions and topology of spin-triplet superconductivity: Application to UTe${}_2$
• Topological invariants beyond symmetry indicators: Boundary diagnostics for twofold rotationally symmetric superconductors
• Odd-Parity Spin-Triplet Superconductivity in Centrosymmetric Antiferromagnetic Metals
• Higher-order topological superconductivity in a topological metal 1T${}^{\prime }$-MoTe${}_2$
• Topologically localized insulators
• 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
• Characterization of higher-order topological superconductors using Bott indices
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Higher-order topological superconductors characterized by Fermi level crossings
• Higher-order topological phases for time-reversal-symmetry breaking superconductivity in UTe${}_2$
• Fragile topology in nodal-line semimetal superconductors
• Engineering Majorana corner modes from two-dimensional hexagonal crystals
• Fermi-surface diagnosis for topological superconductivity with $s$-wave-like pairing symmetries
• Nodal higher-order topological superconductivity from C6-symmetric Dirac semimetals