Fig. 2: Two-dimensional HOTI material BiSe (in the GaSe prototype).

a 2D bulk crystal structure top and side views. The inset shows the Brillouin zone high-symmetry points. b Bulk band-structure along the high symmetry lines and the spin Hall conductivity (\({\sigma }_{xy}^{z}\)) as a function of the energy. The dashed blue line represents the Fermi level. The gray shaded area encompass the bulk band gap. Green and purple dots represent states with C3 eigenvalues \({\gamma }_{{C}_{3}}=-\pi\) or ±π/3, respectively. Filled and unfilled dots represent + and − parity eigenvalues (ξi = ±1) for each occupied band at the TRIM K-points. c Energy eigenvalues of a triangular flake with edges of approximately 50 Å. The localized corner modes are highlighted in red. d Flake structure with corner states charge density highlighted in blue.