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Finite size effects on hinge states in three-dimensional second-order topological insulators

Penglei WangYong-Lian ZouJuntao Song
Dec 2022
摘要
We investigate the finite size effects of a three-dimensional second-ordertopological insulator with fourfold rotational symmetry and time-reversalsymmetry. Starting from the effective Hamiltonian of the three-dimensionalsecond-order topological insulator, we derive the effective Hamiltonian of fourtwo-dimensional surface states with gaps derived by perturbative methods. Then,the sign alternation of the mass term of the effective Hamiltonian on theadjacent surface leads to the hinge state. In addition, we obtain the effectiveHamiltonian and its wave function of one-dimensional gapless hinge states withsemi-infinite boundary conditions based on the effective Hamiltonian oftwo-dimensional surface states. In particular, we find that the hinge states onthe two sides of the same surface can couple to produce a finite energy gap.
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