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 (px, py and pz). The essential mechanism can be understood by the fact while in 3D, the pz 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 px-py 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.