Efficient method to compute ${\mathbb{Z}}_4$-indices with glide symmetry and applications to Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$

Abstract

We propose an efficient method to numerically evaluate ${\mathbb{Z}}_4$-indices of Möbius/hourglass topological phases with glide symmetry. Our method directly provides ${\mathbb{Z}}_4$-indices in the lattice Brillouin zone while the existing method requires careful observations of momentum dependent Wannier charge centers. As applications, we perform systematic computation of ${\mathbb{Z}}_4$-indices for Möbius materials, $\mathrm{CeNiSn}$ and $\mathrm{UCoGe}$. In particular, our analysis elucidates that $\mathrm{UCoGe}$ shows strong Möbius superconductivity for the $A_u$- or $B_{3u}$-representation whose topology has not been fully characterized. Furthermore, obtained phase diagrams reveal novel topological gapless excitations in the bulk which are protected by nonsymmorphic glide symmetry. We observe these gapless excitations with glide symmetry by doping holes into the superconducting phase of the $B_{1u}$- or $B_{3u}$-representation.

arXiv comment20 pages, 7 figures, published version

References in corpus (50)

• Topological Insulators
• Topological insulators and superconductors
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Unpaired Majorana fermions in quantum wires
• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• A topological Dirac insulator in a quantum spin Hall phase : Experimental observation of first strong topological insulator
• Classification of topological insulators and superconductors in three spatial dimensions
• New directions in the pursuit of Majorana fermions in solid state systems
• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Topological Crystalline Insulators
• Periodic table for topological insulators and superconductors
• Crossover of Three-Dimensional Topological Insulator of Bi2Se3 to the Two-Dimensional Limit
• Topological Crystalline Insulators in the SnTe Material Class
• Chern Numbers in Discretized Brillouin Zone: Efficient Method of Computing (Spin) Hall Conductances
• Observation of the fractional ac Josephson effect: the signature of Majorana particles
• Experimental realization of a topological crystalline insulator in SnTe
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• Topological Superconductivity in CuxBi2Se3
• Quantum Spin Hall Effect and Topologically Invariant Chern Numbers
• Topological classification of crystalline insulators through band structure combinatorics
• Computing topological invariants without inversion symmetry
• Wannier representation of Z_2 topological insulators
• Hourglass Fermions
• Majorana Fermions and Topology in Superconductors
• Topology of Andreev Bound States with Flat Dispersion
• Bulk-boundary correspondence of topological insulators from their Green's functions
• Topological odd-parity superconductors
• Topological phases and surface flat bands in superconductors without inversion symmetry
• Weyl superconductors
• Quantum spin Hall effect in three dimensional materials: Lattice computation of Z${}_2$ topological invariants and its application to Bi and Sb
• The strong side of weak topological insulators
• Topological superconductivity in bilayer Rashba system
• Topology, Delocalization via Average Symmetry and the Symplectic Anderson Transition
• Topological Crystalline Kondo Insulator in Mixed Valence Ytterbium Borides
• Topology of nonsymmorphic crystalline insulators and superconductors
• Experimental Discovery of the First Nonsymmorphic Topological Insulator KHgSb
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Quantum transport and two-parameter scaling at the surface of a weak topological insulator
• Surface density of states and topological edge states in non-centrosymmetric superconductors
• Statistical Topological Insulators
• Pair-density wave states through spin-orbit coupling in multilayer superconductors
• Möbius Kondo Insulators
• Möbius topological superconductivity in UPt${}_3$
• $Z_4$ Topological Superconductivity in UCoGe
• Majorana flat bands, chiral Majorana edge states, and unidirectional Majorana edge states in noncentrosymmetric superconductors
• Symmetry enforced line nodes in unconventional superconductors
• Symmetry-protected line nodes and Majorana flat bands in nodal crystalline superconductors
• Electronic structures of ferromagnetic superconductors ${\mathrm{UGe}}_2$ and $\mathrm{UCoGe}$ studied by angle-resolved photoelectron spectroscopy
• Fate of Majorana modes in ${\mathrm{CeCoIn}}_5$/${\mathrm{YbCoIn}}_5$ superlattices -a test bed for reduction of topological classification-

Cited by in corpus (14)

• Unconventional Superconductivity in UTe2
• Insulator-metal transition and topological superconductivity in UTe2 from a first-principles calculation
• Interplay between altermagnetism and nonsymmorphic symmetries generating large anomalous Hall conductivity by semi-Dirac points induced anticrossings
• $Z_4$ Topological Superconductivity in UCoGe
• Multiple band-crossings and Fermi surface topology: role of double nonsymmorphic symmetries in MnP-type crystal structures
• Majorana multipole response: General theory and application to wallpaper groups
• Magnetic response of Majorana Kramers pairs with an order-two symmetry
• Topological gapless points in superconductors: From the viewpoint of symmetry
• Majorana multipole response with magnetic point group symmetry
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Local symmetry groups for arbitrary wavevectors
• Inelastic neutron scattering and muon spin relaxation investigations of the deuterated Kondo lattices CeNiSnD${}_x$
• Superconducting Gap Structures in Wallpaper Fermion Systems
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals