Topological non-symmorphic crystalline insulators

Abstract

In this work, we identify a new class of Z2 topological insulator protected by non-symmorphic crystalline symmetry, dubbed a "topological non-symmorphic crystalline insulator". We construct a concrete tight-binding model with the non-symmorphic space group pmg and confirm the topological nature of this model by calculating topological surface states and defining a Z2 topological invariant. Based on the projective representation theory, we extend our discussion to other non-symmorphic space groups that allows to host topological non-symmorphic crystalline insulators.

7 pages, 5 figures

References in corpus (8)

• Topological Insulators with Inversion Symmetry
• Experimental Observation of the Quantum Anomalous Hall Effect in a Magnetic Topological Insulator
• Topological Crystalline Insulators
• Magnetic Order versus superconductivity in the Iron-based layered La(O1-xFx)FeAs systems
• Antiferromagnetic topological insulators
• The space group classification of topological band insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Bi-collinear antiferromagnetic order in the tetragonal $\alpha$-FeTe

Cited by in corpus (101)

• Classification of topological quantum matter with symmetries
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Topological nodal line semimetals with and without spin-orbital coupling
• Topological Crystalline Insulators and Topological Superconductors: From Concepts to Materials
• Topological classification of crystalline insulators through band structure combinatorics
• Topology of crystalline insulators and superconductors
• High-throughput calculations of magnetic topological materials
• Hourglass Fermions
• Three-dimensional topological photonic crystal with a single surface Dirac cone
• Classification of topological phonons in linear mechanical metamaterials
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• New classes of topological crystalline insulators with unpinned surface Dirac cones
• Möbius Insulator and Higher-Order Topology in MnBi${}_{2n}$Te${}_{3n+1}$
• Topological semimetals with Riemann surface states
• Z2-topology in nonsymmorphic crystalline insulators: Mobius twist in surface states
• Topology of nonsymmorphic crystalline insulators and superconductors
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• Rotation Anomaly and Topological Crystalline Insulators
• Topological Insulators from Group Cohomology
• Nonsymmorphic symmetry-required band crossings in topological semimetals
• Berry-phase description of Topological Crystalline Insulators
• Topological Phases in the Single-Layer FeSe
• Band Connectivity for Topological Quantum Chemistry: Band Structures As A Graph Theory Problem
• Topological charges of three-dimensional Dirac semimetals with rotation symmetry
• Fragile Phases As Affine Monoids: Classification and Material Examples
• Topological Bloch oscillations
• ${\mathbb{Z}}_2$ Topological Invariant for Magnon Spin Hall Systems
• Crystallographic splitting theorem for band representations and fragile topological photonic crystals
• Classification of topological crystalline insulators based on representation theory
• Three-dimensional superconductors with hybrid higher order topology
• Topological classification and diagnosis in magnetically ordered electronic materials
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• Topologically stable gapless phases in nonsymmorphic superconductors
• Atiyah-Hirzebruch Spectral Sequence in Band Topology: General Formalism and Topological Invariants for 230 Space Groups
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Non-Hermiticity and topological invariants of magnon Bogoliubov-de Gennes systems
• Line nodes, Dirac points and Lifshitz transition in 2D nonsymmorphic photonic crystals
• Filling-Enforced Quantum Band Insulators in Spin-Orbit Coupled Crystals
• Symmetry Protected Topological Superfluid ${}^3$He-B
• Hourglass Fermion Surface States in Stacked Topological Insulators with Nonsymmorphic Symmetry
• Weyl semimetal from spontaneous inversion symmetry breaking in pyrochlore oxides
• Perspective: Strongly correlated and topological states in [111] grown transition metal oxide thin films and heterostructures
• Hourglass semimetals with nonsymmorphic symmetries in three dimensions
• Topological Nonsymmorphic Crystalline Superconductors
• Delocalization Transition of Disordered Axion Insulator
• Application of the induction procedure and the Smith Decomposition in the calculation and topological classification of electronic band structures in the 230 space groups
• Field-direction control of the type of charge carriers in nonsymmorphic IrO2
• Electronic properties of SnTe-class topological crystalline insulator materials
• Fractional chiral superconductors
• No-go theorem for topological insulators and sure-fire recipe for Chern insulators
• Topology invisible to eigenvalues in obstructed atomic insulators
• Phononic topological insulators with tunable pseudospin physics
• Unusual change in the Dirac-cone energy band upon two-step magnetic transition in CeBi
• Disorder-Induced Weyl Semimetal Phase and Sequential Band Inversions in PbSe-SnSe Alloys
• Glide-symmetric magnetic topological crystalline insulators with inversion symmetry
• Higher-order Klein bottle topological insulator in three-dimensional acoustic crystals
• Higher-Order Topological Insulators via Momentum-Space Nonsymmorphic Symmetries
• Universal Relation among Many-Body Chern Number, Rotation Symmetry, and Filling
• Space group constraints on weak indices in topological insulators
• Topological Gapless Phases in Non-Symmorphic Antiferromagnets
• Organizing symmetry-protected topological phases by layering and symmetry reduction: a minimalist perspective
• 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
• Novel topological insulators from crystalline symmetries
• Extremely large magnetoresistance in the hourglass Dirac loop chain metal β-ReO${}_2$
• Topological corner modes in a brick lattice with nonsymmorphic symmetry
• Catalog of noninteracting tight-binding models with two energy bands in one dimension
• Glide-symmetric topological crystalline insulator phase in a nonprimitive lattice
• Rational boundary charge in one-dimensional systems with interaction and disorder
• Topological Nonsymmorphic Ribbons out of Symmorphic Bulk
• Interacting topological mirror excitonic insulator in one dimension
• Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice
• Anderson Critical Metal Phase in Trivial States Protected by Average Magnetic Crystalline Symmetry
• Protected Gapless Edge States In Trivial Topology
• Anomalous Crystal Shapes of Topological Crystalline Insulators
• Surface-dependent Majorana vortex phases in topological crystalline insulators
• Hidden-symmetry-protected Z_2 topological insulator in a cubic lattice
• Hidden-symmetry-protected quantum pseudo-spin Hall effect in optical lattices
• Theory of Anomalous Floquet Higher-Order Topology: Classification, Characterization, and Bulk-Boundary Correspondence
• Topological crystalline protection in a photonic system
• Fractionalizing glide reflections in two-dimensional Z2 topologically ordered phases
• Kitaev Building-block Construction for Inversion-Protected Higher-order Topological Superconductors
• Effects of first- and second-order topological phases on equilibrium crystal shapes
• Nonsymmorphic bosonization in one-dimensional generalized Kitaev spin-1/2 models
• $Z_2$ antiferromagnetic topological insulators with broken $C_4$ symmetry
• Non-Hermitian ${\mathbb{Z}}_4$ skin effect protected by glide symmetry
• Stability against contact interactions of a topological superconductor in two-dimensional space protected by time-reversal and reflection symmetries
• Nonsymmorphic spin-space cubic groups and SU(2)${}_1$ conformal invariance in one-dimensional spin-1/2 models
• Hall effect of ferro/antiferromagnetic wallpaper fermions
• Optically Induced Topological Phase Transition in two dimensional Square Lattice Antiferromagnet
• Topological nonsymmorphic insulator versus Dirac semimetal in KZnBi
• One-dimensional ${\mathbb{Z}}_4$ topological superconductor
• Intrinsic (Axion) Statistical Topological Insulator
• Quantum spin Hall effect in bilayer honeycomb lattices with C-type antiferromagnetic order
• Magnon-mediated superconductivity on ferromagnetic wallpaper fermions
• Interacting Crystalline Topological Insulators in two-dimensions with Time-Reversal Symmetry
• Disorder-induced delocalization and reentrance in a Chern-Hopf insulator
• Hidden wallpaper fermion and third-order topological insulator
• Glide-resolved photoemission spectroscopy: Measuring topological invariants in nonsymmorphic space groups
• One-dimensional topology and topolectrics of nonsymmorphic Kramers degenerate systems
• Dynamical Symmetry Indicators for Floquet Crystals