Real-space Obstruction in Quantum Spin Hall Insulators

Abstract

The recently introduced classification of two-dimensional insulators in terms of topological crystalline invariants has been applied so far to "obstructed" atomic insulators characterized by a mismatch between the centers of the electronic Wannier functions and the ionic positions. We extend this notion to quantum spin Hall insulators in which the ground state cannot be described in terms of time-reversal symmetric localized Wannier functions. A system equivalent to graphene in all its relevant electronic and topological properties except for a real-space obstruction is identified and studied via symmetry analysis as well as with density functional theory. The low-energy model comprises a local spin-orbit coupling and a non-local symmetry breaking potential, which turn out to be the essential ingredients for an obstructed quantum spin Hall insulator. An experimental fingerprint of the obstruction is then measured in a large-gap triangular quantum spin Hall material.

arXiv comment9 pages, 6 figures and 1 table. Supplementary material: 5 pages, 4 figures and 2 tables

References in corpus (42)

• Topological Insulators
• Quantum Spin Hall Effect in Graphene
• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Quantum Spin Hall Insulator State in HgTe Quantum Wells
• Topological Insulators in Three Dimensions
• Topological Insulators with Inversion Symmetry
• Quantized Electric Multipole Insulators
• Higher-Order Topological Insulators
• Topological quantum chemistry
• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• Low-energy effective Hamiltonian involving spin-orbit coupling in Silicene and Two-Dimensional Germanium and Tin
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Bismuthene on a SiC Substrate: A Candidate for a New High-Temperature Quantum Spin Hall Paradigm
• Spin-orbit gap of graphene: First-principles calculations
• Reflection symmetric second-order topological insulators and superconductors
• Time Reversal Polarization and a Z_2 Adiabatic Spin Pump
• An equivalent expression of Z2 Topological Invariant for band insulators using Non-Abelian Berry's connection
• Higher-Order Topology in Bismuth
• Symmetry-based Indicators of Band Topology in the 230 Space Groups
• Quantization of fractional corner charge in $C_n$-symmetric higher-order topological crystalline insulators
• Topological classification of crystalline insulators through band structure combinatorics
• Computing topological invariants without inversion symmetry
• Wannier representation of Z_2 topological insulators
• Exponential localization of Wannier functions in insulators
• On the $Z_2$ classification of Quantum Spin Hall Models
• Building Blocks of Topological Quantum Chemistry: Elementary Band Representations
• Disordered Topological Insulators via $C^{\ast }$-Algebras
• Higher-order topological insulators protected by inversion and rotoinversion symmetries
• Model spin-orbit coupling Hamiltonians for graphene systems
• Rotation Anomaly and Topological Crystalline Insulators
• Triviality of Bloch and Bloch-Dirac bundles
• Topology of Disconnected Elementary Band Representations
• Fractional corner charges in spin-orbit coupled crystals
• Smooth gauge for topological insulators
• Orbital-driven Rashba effect in a binary honeycomb monolayer AgTe
• Obstructed surface states as the origin of catalytic activity in inorganic heterogeneous catalysts
• Bulk-corner correspondence of time-reversal symmetric insulators: deduplicating real-space invariants
• On the topological immunity of corner states in two-dimensional crystalline insulators
• Filling anomaly for general 2D and 3D $C_4$ symmetric lattices
• Filling-Enforced Quantum Band Insulators in Spin-Orbit Coupled Crystals
• Design and realization of topological Dirac fermions on a triangular lattice
• The hybrid-order topology of weak topological insulators

Cited by in corpus (6)

• Stabilizing an atomically thin quantum spin Hall insulator at ambient conditions: Graphene-intercalation of indenene
• Spin Hall conductivity in the Kane-Mele-Hubbard model at finite temperature
• A mono-atomic orbital-based 1D topological crystalline insulator
• Recipe for higher-order topology on the triangular lattice
• Atomically thin obstructed atomic insulators with robust edge modes and quantized spin Hall effect
• Engineering correlated Dirac fermions and flat bands on SiC with transition-metal adatom lattices