Figure 3
DFT simulation of the Sb41 model, which consists of 41 (111) planes. In the initial model, one of the surfaces is terminated by a bilayer while the other surface is terminated by a single plane with dangling covalent bonds. (a) The interplanar distances along the [111] direction. The dashed blue horizontal lines highlight the bulk-like interplanar distances, while the dashed gray horizontal line highlights the interplanar distance of the cubic phase of Sb. The black circles indicate the DFT calculation while the red circles indicate the fit from Eq. (2), which describes a TS in the SSH model. The two-dimensional defect at the surface, in the form of a (111) plane with dangling covalent bonds, results in a considerable structural distortion. (b) Spatial charge density distribution of the electron dispersion branches (marked in color) of electrons at the Г point of the Brillouin zone. (c) Spatial distribution of the Fermi level DOS averaged over (111) planes. The planes are aligned with (a,b). The soliton region sees an order of magnitude increase in the DOS at the Fermi level. The black arrow indicates the position of the TS center, n0, while the rectangle indicates the TS size, w, obtained from Eq. (2). (d) DFT calculation of the electron dispersion in the M–Г–К direction without considering the SOI. (e) Zoom of the red square in (d). Four dispersion bands are highlighted by red, blue, dark green and light green. Their spatial distribution within the slab can be visualized in (b). The red and blue bands are TS soliton states while the two green bands are surface states at either side of the slab. Note the non-equivalence of the two surfaces due to the proximity of one of the surfaces to the TS. (f) The interplanar distances along the [111] direction. The sinusoid represents the alternating interplanar distance of bulk Sb. The half-filled part indicates the van der Waals distance of 2.31 Å. As one passes through the TS region, the interplanar distance undergoes a phase change of π.
