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arXiv · 1308.4278

Topological Kirchhoff Law and Bulk-Edge Correspondence for Valley-Chern and Spin-Valley-Chern Numbers

Motohiko Ezawa
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Abstract

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. The edge state between them is topologically trivial in the tight-binding model but is shown to be as robust as the topological edge. 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.

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Motohiko Ezawa. 2013-08-20. Topological Kirchhoff Law and Bulk-Edge Correspondence for Valley-Chern and Spin-Valley-Chern Numbers. https://doi.org/10.1103/physrevb.88.161406

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