Formation of a large gap quantum spin Hall phase in a 2D trigonal lattice with three p-orbitals

The quantum spin Hall (QSH) phase in a trigonal lattice requires typically a minimal basis of three orbitals with one even parity s and two odd parity p orbitals. Here, based on first-principles calculations combined with tight-binding model analyses and calculations, we demonstrate that depositing 1/3 monolayer Bi or Te atom layers on an existing experimental Ag/Si(111) surface can produce a QSH phase readily but with three p-orbitals (p_x, p_y and p_z). The essential mechanism can be understood by the fact while in 3D, the p_z orbital has an odd parity, its parity becomes even when it is projected onto a 2D surface so as to act in place of the s orbital in the original minimum basis. Furthermore, non-trivial large gaps, i.e., 275.0 meV for Bi and 162.5 meV for Te systems, arise from a spin-orbit coupling induced quadratic p_x-p_y band opening at the Γ point. Our findings will significantly expand the search for a substrate supported QSH phase with a large gap, especially in the Si surface, to new orbital combinations and hence new elements.