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.

46 pages, 1 figure

References in corpus (4)

• Classification of topological insulators and superconductors in three spatial dimensions
• The bulk-edge correspondence for the quantum Hall effect in Kasparov theory
• Toeplitz operators on concave corners and topologically protected corner states
• '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