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arXiv · 2109.06412

Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators

Yuki Nagasato·Yositake Takane·Yukinori Yoshimura·Shin Hayashi·Takeshi Nakanishi
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Abstract

A second-order topological insulator on a two-dimensional square lattice hosts zero-dimensional states inside a band gap. They are localized near $90^{\circ}$ and $270^{\circ}$ corners constituting an edge of the system. When the edge is in a staircase form consisting of these two corners, two families of edge states (i.e., one-dimensional states localized near the edge) appear as a result of the hybridization of zero-dimensional states. We identify symmetry that makes them gapless. We also show that a pair of nontrivial winding numbers associated with this symmetry guarantee a gapless spectrum of edge states, indicating that bulk--boundary correspondence holds in this topological insulator with a staircase edge.

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Yuki Nagasato, Yositake Takane, Yukinori Yoshimura, Shin Hayashi, Takeshi Nakanishi. 2021-09-14. Gapless States Localized along a Staircase Edge in Second-Order Topological Insulators. https://doi.org/10.7566/jpsj.90.104703

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