Traveling edge states in massive Dirac equations along slowly varying edges

Pipi Hu Yau Mathematical Sciences Center, Tsinghua University, Beijing, 100084, China Peng Xie Yi Zhu Yau Mathematical Sciences Center and Department of Mathematical Sciences, Tsinghua University, Beijing, 100084, China

Analysis of PDEs mathscidoc:2204.03003

2022.2
Edge states attract more and more research interests owing to the novel topologically protected properties. In this work, we studied edge modes and traveling edge states via the linear Dirac equation with so-called edge-admissible masses. The unidirectional edge state provides a heuristic approach to more general traveling edge states through the localized behavior along slowly varying edges. We show the dominated asymptotic solutions of two typical edge states that follow circular and curved edges with small curvature by the analytic and quantitative arguments.
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@inproceedings{pipi2022traveling,
  title={Traveling edge states in massive Dirac equations along slowly varying edges},
  author={Pipi Hu, Peng Xie, and Yi Zhu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422141721834915098},
  year={2022},
}
Pipi Hu, Peng Xie, and Yi Zhu. Traveling edge states in massive Dirac equations along slowly varying edges. 2022. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20220422141721834915098.
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