Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states

Abstract

It has been known that an anti-unitary symmetry such as time-reversal or charge conjugation is needed to realize Z2 topological phases in non-interacting systems. Topological insulators and superconducting nanowires are representative examples of such Z2 topological matters. Here we report the first-known Z2 topological phase protected by only unitary symmetries. We show that the presence of a nonsymmorphic space group symmetry opens a possibility to realize Z2 topological phases without assuming any anti-unitary symmetry. The Z2 topological phases are constructed in various dimensions, which are closely related to each other by Hamiltonian mapping. In two and three dimensions, the Z2 phases have a surface consistent with the nonsymmorphic space group symmetry, and thus they support topological gapless surface states. Remarkably, the surface states have a unique energy dispersion with the Mobius twist, which identifies the Z2 phases experimentally. We also provide the relevant structure in the K-theory.

10 pages, 5 figures

References in corpus (13)

• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Topological Insulators with Inversion Symmetry
• Classification of topological insulators and superconductors in three spatial dimensions
• Topological Crystalline Insulators
• Three dimensional topological invariants for time reversal invariant Hamiltonians and the three dimensional quantum spin Hall effect
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Non-Abelian Topological Order in S-Wave Superfluids of Ultracold Fermionic Atoms
• The space group classification of topological band insulators
• Topological Phases of Noncentrosymmetric Superconductors: Edge States, Majorana Fermions, and the Non-Abelian Statistics
• Topology of crystalline insulators and superconductors
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Topological properties of spin-triplet superconductors and the Fermi surface topology in the normal state
• Symmetry Protected Topological Order and Spin Susceptibility in Superfluid 3He-B

Cited by in corpus (54)

• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• All Topological Bands of All Nonmagnetic Stoichiometric Materials
• Projectively enriched symmetry and topology in acoustic crystals
• Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
• Brillouin Klein Bottle From Artificial Gauge Fields
• Topological crystalline superconductivity in locally noncentrosymmetric CeRh${}_2$As${}_2$
• Topologically stable gapless phases in nonsymmorphic superconductors
• Floquet topological phase transitions in a periodically quenched dimer
• Hourglass Fermion Surface States in Stacked Topological Insulators with Nonsymmorphic Symmetry
• Möbius topological superconductivity in UPt${}_3$
• Symmetry indicator in non-Hermitian systems
• Interplay of non-symmorphic symmetry and spin-orbit coupling in hyperkagome spin liquids: Applications to Na${}_4$Ir${}_3$O${}_8$
• Intrinsic Magnetic Topological Materials
• Fractional chiral superconductors
• Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• Multiorbital edge and corner states in black phosphorene
• Non-Abelian Braiding of Topological Edge Bands
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions
• A gap-protected zero-Hall effect state in the quantum limit of the nonsymmorphic metal KHgSb
• Weyl points on non-orientable manifolds
• Extremely large magnetoresistance in the hourglass Dirac loop chain metal β-ReO${}_2$
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• Correlation-induced Fermi surface evolution and topological crystalline superconductivity in CeRh2As2
• Nonsymmorphic chiral symmetry and solitons in the Rice-Mele model
• Non-Hermitian Origin of Detachable Boundary States in Topological Insulators
• Signature of topological non-trivial band structure in Ta${}_3$SiTe${}_6$
• Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice
• Revealing the spatial nature of sublattice symmetry
• Light-induced ultrafast glide-mirror symmetry breaking in black phosphorus
• Anomalous Crystal Shapes of Topological Crystalline Insulators
• Chern dartboard insulator: sub-Brillouin zone topology and skyrmion multipoles
• $Z_2$ Dirac points with topologically protected multihelicoid surface states
• Pentagonal nanowires from topological crystalline insulators: a platform for intrinsic core-shell nanowires and higher-order topology
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Theoretical analysis of glide-Z_2 magnetic topological photonic crystals
• A Solvable Model for Discrete Time Crystal Enforced by Nonsymmorphic Dynamical Symmetry
• Diversified Ruderman-Kittel-Kasuya-Yosida Interactions in a Nonsymmorphic Crystal
• Parallel and anti-parallel helical surface states for topological semimetals
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Intrinsic (Axion) Statistical Topological Insulator
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Symmetry-Protected Solitons and Bulk-Boundary Correspondence in Generalized Jackiw-Rebbi Models
• Non-Abelian geometry, topology, and dynamics of a nonreciprocal Su-Schrieffer-Heeger ladder
• Local symmetry groups for arbitrary wavevectors
• Floquet Möbius topological insulators
• Fragile topological insulators protected by rotation symmetry without spin-orbit coupling
• Topological analog of the magnetic bit within the Su-Schrieffer-Heeger-Holstein model
• Solitons in binary compounds with stacked two-dimensional honeycomb lattices
• Crystalline finite-size topology
• Hidden wallpaper fermion and third-order topological insulator
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Magnetic-Field Tunable Möbius and Higher-Order Topological Insulators in Three-Dimensional Layered Octagonal Quasicrystals