Regular Article

Substrate effect on edge states of a quantum spin Hall insulator in Kane–Mele model

Department of Physics, Ewha Womans University, Seoul 03760, Korea

^a Present address: Department of Physics, University of Seoul, Seoul 02504, Korea
^b e-mail: gsjeon@ewha.ac.kr

Received: 19 November 2018
Received in final form: 11 March 2019
Published online: 23 April 2019

Abstract

We investigate the topological phases and the edge states of a quantum spin Hall insulator of the Kane–Mele model placed on top of a two-dimensional normal insulator caused by the staggered lattice potential. We show that, in the parameter space of interlayer hopping and the staggered lattice potential, there occurs a topological phase transition between the two phases, topological and normal insulating phases. Effective Hamiltonian for the edge states is constructed and it is verified that it reproduces well the edge-state energy dispersion in the presence of small interlayer hopping. Finally, we estimate the edge-state width by fitting the probability densities numerically and discuss how the edge-state width changes near the phase boundary and in an asymptotic region.