Abstract
Functionalized X-Bi bilayers (X = Ga, In, and Tl) with halogens bonded on their both sides have been recently claimed to be the giant topological insulators due to the strong band inversion strengths. Employing the first-principles electronic structure calculation, we find the topological band order transition from the order p – p – s of the X-Bi bilayers with halogens on their both sides to the new order p – s – p of the bilayers (especially for X = Ga and In) with halogen on one side and hydrogen on the other side, where the asymmetric hydrogen bonding simulates the substrate. We further find that the p – s bulk band gap of the bilayer bearing the new order p – s – p sensitively depends on the electric field, which enables a meaningful engineering of the quantum spin Hall edge state by controlling the external electric field.
Highlights
We have analyzed the topological band order transition from p – p – s to p – s – p occurring in the route from Y-X-Bi-Y to Y-X-Bi-H
The s orbitals at Γv1 of F-GaBi-H and F-InBi-H are strongly hybridized with the px/y and pz orbitals so that their energetics become sensitive to the structural deformation, which leads to the band order transition and results in the p – s bulk band gap
The p – s bulk band gap is found highly responsive to the external electric field, which would enable an engineering of the quantum spin Hall edge transport
Summary
We have performed the first-principles electronic structure calculation of Y-X-Bi-H (X =group III elements like Ga, In, and Tl and Y =halogens like F, Cl, Br, and I) to simulate the substrate-supported functionalized bilayers. We have analyzed the topological band order transition from p – p – s to p – s – p occurring in the route from Y-X-Bi-Y to Y-X-Bi-H (especially for X =Ga and In).
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