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.

Graphical abstract

中文翻译：

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蜂窝状晶格绝缘体的拓扑相变和电导

摘要

拓扑晶体绝缘体（TCI）代表了一种新的量子物质状态，该状态在晶体上受到晶体对称性的保护。我们构建了具有C _3-对称蜂窝晶格的2D TCI薄膜的最小紧束缚模型。在高对称点K，K ^'上观察到四个Dirac锥和Γ点，考虑基本术语自旋轨道相互作用。通过引入质量项，可以打开狄拉克间隙以触发拓扑相变。然后，我们用数值方法研究了由之字形和扶手椅状纳米带组成的TCI薄膜的能带结构，电导率和状态的局部密度。结果表明，无间隙拓扑边缘状态与非零镜像Chern数之间存在一一对应关系。最后，我们施加垂直于TCI膜的外部电场，这会破坏镜像对称性。结果，非平凡的边缘模式被破坏，电导被电场关闭。

图形概要