Coupled-layer description of topological crystalline insulators

Abstract

We introduce a coupled-layer construction to describe three-dimensional topological crystalline insulators protected by reflection symmetry. Our approach uses stacks of weakly-coupled two-dimensional Chern insulators to produce topological crystalline insulators in one higher dimension, with tunable number and location of surface Dirac cones. As an application of our formalism, we turn to a simplified model of topological crystalline insulator SnTe, showing that its protected surface states can be described using the coupled layer construction.

11 pages, 6 figures. This is the final, published version

References in corpus (14)

• Topological Crystalline Insulators
• Topological Defects and Gapless Modes in Insulators and Superconductors
• Antiferromagnetic topological insulators
• The space group classification of topological band insulators
• Bulk Topological Invariants in Noninteracting Point Group Symmetric Insulators
• Classification of reflection symmetry protected topological semimetals and nodal superconductors
• Crystal Field Effect Induced Topological Crystalline Insulators In Monolayer IV-VI Semiconductors
• Theory of interacting topological crystalline insulators
• Classification of topological crystalline insulators based on representation theory
• Bulk invariants and topological response in insulators and superconductors with nonsymmorphic symmetries
• From an array of quantum wires to three-dimensional fractional topological insulators
• Layered Topological Crystalline Insulators
• Extended topological group structure due to average reflection symmetry
• Correlation effects on topological crystalline insulators

Cited by in corpus (26)

• Higher-Order Topological Insulators
• Quantitative mappings between symmetry and topology in solids
• Higher-order bulk-boundary correspondence for topological crystalline phases
• Building crystalline topological phases from lower-dimensional states
• Real Space Invariants: Twisted Bulk-Boundary Correspondence of Fragile Topology
• Rotation Anomaly and Topological Crystalline Insulators
• Shift insulators: rotation-protected two-dimensional topological crystalline insulators
• Higher-order topological band structures
• Inversion-symmetry protected chiral hinge states in stacks of doped quantum Hall layers
• Computation of topological phase diagram of disordered Pb${}_{1-x}$Sn${}_x$Te using the kernel polynomial method
• Chiral Hinge Magnons in Second-Order Topological Magnon Insulators
• Topological Zero-Dimensional Defect and Flux States in Three-Dimensional Insulators
• Constructing higher-order topological states in higher dimension
• Topological Crystalline Magnets: Symmetry-Protected Topological Phases of Fermions
• Surface Magnetism in Topological Crystalline Insulators
• Anomalous Floquet topological crystalline insulators
• Topological crystalline insulators from stacked graphene layers
• Classification and surface anomaly of glide symmetry protected topological phases in three dimensions
• Reentrance of Topological Phase in Spin-1 Frustrated Heisenberg Chain
• Anomalous Crystal Shapes of Topological Crystalline Insulators
• Topological electronic structure of twin boundaries and twinning superlattices in the SnTe material class
• Spin Stiffness and Domain Walls in Dirac-Electron Mediated Magnets
• Coexisting surface states in the weak and crystalline topological insulator Bi_2TeI
• Exceptional second-order topological insulators
• Mirror Chern numbers in the hybrid Wannier representation
• Artificial oxide heterostructures with non-trivial topology