Boundary condition analysis of first and second order topological insulators

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.

Automated summary

We analytically study the boundary conditions of Dirac fermion models on a lattice, focusing on the first and second order topological insulators. By solving these boundary conditions, we obtain the dispersion relations of edge and hinge states. We clarify the constraint on boundary conditions imposed by the symmetry of the Hamiltonian. Furthermore, we demonstrate the edge-hinge analog of the bulk-edge correspondence, showing that the nontrivial topology of the gapped edge state ensures the gaplessness of the hinge state.