Classification of topological invariants related to corner states

Abstract

We discuss some bulk-surfaces gapped Hamiltonians on a lattice with corners and propose a periodic table for topological invariants related to corner states aimed at studies of higher-order topological insulators. Our table is based on four things: (1) the definition of topological invariants, (2) a proof of their relation with corner states (3) computations of K-groups and (4) a construction of explicit examples.

arXiv comment46 pages, 1 figure

References in corpus (29)

• $Z_2$ Topological Order and the Quantum Spin Hall Effect
• Classification of topological insulators and superconductors in three spatial dimensions
• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Quantized Electric Multipole Insulators
• Periodic table for topological insulators and superconductors
• Higher-Order Topological Insulators
• The Non-Commutative Geometry of the Quantum Hall Effect
• Higher-order topological insulators and superconductors protected by inversion symmetry
• Second-order topological insulators and superconductors with an order-two crystalline symmetry
• Bulk and Boundary Invariants for Complex Topological Insulators: From K-Theory to Physics
• Twisted equivariant matter
• Controlled topological phases and bulk-edge correspondence
• On the K-theoretic classification of topological phases of matter
• Second-order topological phases protected by chiral symmetry
• The $K$-theoretic bulk-edge correspondence for topological insulators
• ${\mathbb{Z}}_Q$ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
• Edge-of-edge States
• Topological classification under nonmagnetic and magnetic point group symmetry: Application of real-space Atiyah-Hirzebruch spectral sequence to higher-order topology
• Index pairings in presence of symmetries with applications to topological insulators
• Topological invariants and corner states for Hamiltonians on a three-dimensional lattice
• Bulk-boundary correspondence for disordered free-fermion topological phases
• Bulk-edge and bulk-hinge correspondence in inversion-symmetric insulators
• The bulk-edge correspondence for the quantum Hall effect in Kasparov theory
• T-duality simplifies bulk-boundary correspondence
• Spectral flows of dilations of Fredholm operators
• Toeplitz operators on concave corners and topologically protected corner states
• The KO-valued spectral flow for skew-adjoint Fredholm operators
• Parity flow as ${\mathbb{Z}}_2$-valued spectral flow
• 'Real' gerbes and Dirac cones of topological insulators

Cited by in corpus (5)

• Local invariants identify topology in metals and gapless systems
• Wannier Topology and Quadrupole Moments for a generalized Benalcazar-Bernevig-Hughes Model
• An index theorem for quarter-plane Toeplitz operators via extended symbols and gapped Invariants related to corner states
• C*-framework for higher-order bulk-boundary correspondences
• Bulk-boundary correspondence in topological two-dimensional non-Hermitian systems: Toeplitz operators and singular values