Hierarchical zero- and one-dimensional topological states in symmetry-controllable grain boundary.

Jang, Won-Jun; Noh, Heeyoon; Kang, Seoung-Hun; Ko, Wonhee; Ku, JiYeon; Park, Moon Jip; Kim, Hyo Won · Nat Commun · 2024

basic_science · Level V

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Abstract

Structural imperfections can be a promising testbed to engineer the symmetries and topological states of solid-state platforms. Here, we present direct evidence of hierarchical transitions of zero- (0D) and one-dimensional (1D) topological states in symmetry-enforced grain boundaries (GB) in 1T'-MoTe<sub>2</sub>. Using a scanning tunneling microscope tip press-and-pulse procedure, we construct two distinct types of GBs, which are differentiated by the underlying symmorphic and nonsymmorphic symmetries. The GBs with the nonsymmorphic rotation symmetry harbor first-order topological edge states protected by a nonsymmorphic band degeneracy. On the other hand, the edge state of the symmorphic GBs attains a band gap. More interestingly, the gapped edge state realizes a hierarchical topological phase, evidenced by the additional 0D boundary states at the GB ends. We anticipate our experiments will pioneer the material platform for the hierarchical realization of first-order and higher-order topology.