Topological phase transition and conductance in topological crystalline insulator with honeycomb lattice
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THE EUROPEAN PHYSICAL JOURNAL B
Regular Article
Topological phase transition and conductance in topological crystalline insulator with honeycomb lattice Yun-Lei Sun 1,a , and En-Jia Ye 2,3,b 1 2 3
School of Information and Electrical Engineering, Zhejiang University City College, Hangzhou 310015, P.R. China School of Science, Jiangnan University, Wuxi 214122, P.R. China. Department of Physics, University of Arizona, Tucson, Arizona 85721, USA Received 18 August 2020 / Received in final form 20 September 2020 / Accepted 9 October 2020 Published online 7 December 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 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, K0 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.
1 Introduction Since topological insulator (TI) was discovered experimentally in HgTe quantum wells [1,2], the relations between topology and symmetry have been some of the most interesting topics in modern condensed matter physics over the years [3,4]. TI has gapless surface states with a gapped bulk state, which is topologically protected by Z2 timereversal symmetry. Recently, it was demonstrated that crystal point-group symmetry can also act as fundamental symmetry, and lead to nontrivial topological phases [5–9]. These nontrivial topological phases protected by spatial symmetries like mirror, rotation or glide are so-called topological crystalline insulator (TCI), which is first theoretically predicted in SnTe-class alloys [10]. From then on, many experimental and theoretical studies have been reported to confirm Pb1−x Snx Te alloys of TCI phase with even number of surface Dirac-cone states [11–15]. Pb1−x Snx Te alloys have three kinds of surface states, the [001], [111] and [110] surfaces, which have discrete symmetries CN with N = 4, 6 and 2. Nowadays, materials with different crystal structure, such as Ca2 As-family and α-Bi4 Br4 , are theoretically predicted to harbor TCI states by first-principles calculations [16,17]. Among them, thin films of group III − V compounds with honeycomb structure has attracted much attention. Their novelty in a b
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