Samsung Advanced Institute of Technology

The discovery of topological states localized at the boundaries and dislocations is of paramount importance in the physics of topological phases. Structural imperfections can be a promising testbed to engineer the symmetries and the concomitant topological states, as they genuinely exist in solid-state matters. Here, we present the direct evidence of hierarchical transitions of zero- (0D) and one-dimensional (1D) topological states in symmetry？enforced grain boundaries (GB) of 1T′？MoTe2. Guided by exerted scanning tunneling microscope (STM)？tip press and pulse, 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 the first-order topological edge state protected by nonsymmorphic band degeneracy. On the other hand, the edge state of the symmorphic GBs attains the band gap. More interestingly, the gapped edge state realizes the hierarchical topological phase, shown by the additional 0D boundary states at the GB ends. We anticipate our experiment will pioneer the material platform for the hierarchical realization of the first-order and higher-order topology.