Fig. 3: LDOS maps of SymC2 symmetry–induced 0D modes and their finite length effects, and NonSymC2 symmetry–protected 1D modes.
From: Hierarchical zero- and one-dimensional topological states in symmetry-controllable grain boundary
a STM image of 1T’–MoTe2 with a SymC2 GB surrounded by two NonSymC2 GBs (Vs = –240 mV, I = 0.1 nA). b dI/dV spectra taken at the position indicated by the colored crosses in (a). c, d dI/dV maps obtained over the area shown in (a) for bias voltages Vs = –100, –4, 34 and 200 mV. The dotted white arrows in the upper left indicate S symmetry–induced boundary modes. e STM image of 1T’–MoTe2 with a longer SymC2 GB near NonSymC2 GB GBs (Vs = –240 mV, I = 0.1 nA). f dI/dV maps obtained over the area shown in (e) for bias voltages Vs = –4 and 34mV. g dI/dV spectra taken at the positions indicated by the black, cyan, magenta, and blue dots. h Numerically calculated NonSymC2-SymC2-NonSymC2 junction of the GBs. Due to the non-trivial band gap of the SymC2 boundary, we find the emergence of the higher-order topological boundary states at the end of the SymC2 GBs. i–j Energy spectra of the SymC2 GB in the open and periodic boundary conditions respectively. In the open boundary condition, the one-dimensional boundary harbors the additional zero-dimensional higher-order topological states (red dots). A total of four states appears, and two of them are localized at each end of the chain.
