Regular Article

Topological phase transition and conductance in topological crystalline insulator with honeycomb lattice

¹ School of Information and Electrical Engineering, Zhejiang University City College, Hangzhou 310015, P.R. China
² School of Science, Jiangnan University, Wuxi 214122, P.R. China.
³ Department of Physics, University of Arizona, Tucson, Arizona 85721, USA

^a e-mail: sunyl@zucc.edu.cn
^b e-mail: yeenjia@jiangnan.edu.cn

Received: 18 August 2020
Received in final form: 20 September 2020
Accepted: 9 October 2020
Published online: 7 December 2020

Abstract

Topological crystalline insulators (TCI) represent a new state of quantum matter which is topologically protected by crystalline symmetry. We construct a minimal tight-binding model for 2D thin TCI films with C₃-symmetry honeycomb lattice. Four Dirac cones are observed at the high-symmetry points K, K^′ and Γ points, considering the basic term spin-orbit interaction. By introducing the mass term, Dirac gaps can be opened to trigger the topological phase transition. We then numerically investigate the band structure, conductance and local density of state of the TCI films consisting of zigzag and armchair nanoribbons. The results indicate that there is a one-to-one correspondence between gapless topological edge states and nonzero mirror-Chern number. Finally, we apply an external electric field perpendicular to the TCI films, which breaks mirror symmetry. As a result, the nontrivial edge modes are destroyed, and the conductance is turned off by the electric field.