Edge-Corner Correspondence: Boundary-Obstructed Topological Phases with Chiral Symmetry

Abstract

The bulk-edge correspondence characterizes topological insulators and superconductors. We generalize this concept to the bulk-corner correspondence and the edge-corner correspondence in two dimensions. In the bulk-corner (edge-corner) correspondence, the topological number is defined for the bulk (edge), while the topological phase is evidenced by the emergence of zero-energy corner states. It is shown that the boundary-obstructed topological phases recently proposed are the edge-corner-correspondence type, while the higher-order topological phases are classified into the bulk-corner-correspondence type and the edge-corner-correspondence type. We construct a simple model exhibiting the edge-corner correspondence based on two Chern insulators having the $s$-wave, $d$-wave and $s_{\pm }$-wave pairings. It is possible to define topological numbers for the edge Hamiltonians, and we have zero-energy corner states in the topological phase. The emergence of zero-energy corner states is observable by measuring the impedance resonance in topological electric circuits.

arXiv comment6 pages, 3 figures

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• Direct dynamical characterization of higher-order topological insulators with nested band inversion surfaces
• Higher-order topological phases emerging from the Su-Schrieffer-Heeger stacking
• Bulk-boundary correspondence in disordered higher-order topological insulators
• Topological classification of Higher-order topological phases with nested band inversion surfaces
• Unified characterization for higher-order topological phase transitions
• Orbital shift-induced boundary obstructed topological materials with a large energy gap
• Generating many Majorana corner modes and multiple phase transitions in Floquet second-order topological superconductors
• Multiorder topological superfluid phase transitions in a two-dimensional optical superlattice
• Crystalline-electromagnetic responses of higher order topological semimetals
• Tunable boson-assisted finite-range interaction and engineering Majorana corner modes in optical lattices
• Unveiling Higher-Order Topology via Polarized Topological Charges
• Remote control of spin polarization of topological corner states
• Boundary obstructed topological superconductor in buckled honeycomb lattice under perpendicular electric field
• Majorana corner states in an attractive quantum spin Hall insulator with opposite in-plane Zeeman energy at two sublattice sites
• Tunable symmetry-protected higher-order topological states with fermionic atoms in bilayer optical lattices
• Extrinsic higher-order topological corner states in AB-stacked transition-metal dichalcogenides
• Breakdown of boundary criticality and exotic topological semimetals in $\mathcal{P}\mathcal{T}$-invariant systems
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators
• Proposal for realizing and probing topological crystalline insulators in optical lattices