Boundary Condition Analysis of First and Second Order Topological Insulators

2022/05/06 by Xi Wu, Wu, Xi, Taro Kimura +1
Physics and Astronomy · #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum optics and atomic interactions #Topological Materials and Phenomena

paper · doi:10.48550/arxiv.2205.03035

openalex publication_date 2022/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We analytically study boundary conditions of the Dirac fermion models on a lattice, which describe the first and second order topological insulators. We obtain the dispersion relations of the edge and hinge states by solving these boundary conditions, and clarify that the Hamiltonian symmetry may provide a constraint on the boundary condition. We also demonstrate the edgehinge analog of the bulk-edge correspondence, in which the nontrivial topology of the gapped edge state ensures gaplessness of the hinge state.

Related

• Gapped Boundary Phases of Topological Insulators via Weak Coupling
• A Short Course on Topological Insulators: Band Structure and Edge States in One and Two Dimensions
• Boundary topological insulators and superconductors of Altland-Zirnbauer tenfold classes
• Topological protection of perturbed edge states
• Formalism of general continuum models with boundary conditions, propagation of bound states from nontrivial to trivial topological classes, and the general surface-state structure near one node of a Weyl semimetal