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Topological Kirchhoff law and bulk-edge correspondence for valley Chern and spin-valley Chern numbers

机译：谷Chern和自旋谷Chern数的拓扑基尔霍夫定律和块状边缘对应

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摘要

The valley Chern and spin-valley Chern numbers are the key concepts in valleytronics. They are topological numbers in the Dirac theory but not in the tight-binding model. We analyze the bulk-edge correspondence between the two phases which have the same Chern and spin-Chern numbers but different valley Chern and spin-valley Chern numbers. Though the edge state between them is topologically trivial in the tight-binding model, it is shown to be as robust as the topological one both for zigzag and armchair edges. We construct Y-junctions made of topological edges. They satisfy the topological Kirchhoff law, where the topological charges are conserved at the junction. We may interpret a Y-junction as a scattering process of particles which have four topological numbers. It would be a milestone of future topological electronics.
机译：谷彻恩和自旋谷彻恩数是Valleytronics中的关键概念。它们是狄拉克理论中的拓扑数，而不是严格约束模型中的拓扑数。我们分析了具有相同的Chern和自旋Chern数但具有不同的谷Chern和自旋谷Chern数的两个阶段之间的体积边缘对应关系。尽管在紧密绑定模型中它们之间的边缘状态在拓扑上是微不足道的，但对于锯齿形和扶手椅形边缘，它都表现出与拓扑结构一样强大的状态。我们构造由拓扑边构成的Y型结。它们满足拓扑基尔霍夫定律，其中交点处的拓扑电荷守恒。我们可以将Y结解释为具有四个拓扑数的粒子的散射过程。这将是未来拓扑电子学的一个里程碑。

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