Wu Xi, Kimura Taro
School of Physics and Electronics, Hunan University, Changsha 410082, People's Republic of China.
Institut de Mathématiques de Bourgogne, Université Bourgogne Franche-Comté, Dijon, France.
J Phys Condens Matter. 2022 Oct 18;34(48). doi: 10.1088/1361-648X/ac9815.
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 edge-hinge analog of the bulk-edge correspondence, in which the nontrivial topology of the gapped edge state ensures gaplessness of the hinge state.
