Spin-polarization control driven by a Rashba-type effect breaking the mirror symmetry in two-dimensional dual topological insulators

Three-dimensional topological insulators protected by both the time reversal (TR) and mirror symmetries were recently predicted and observed. Two-dimensional materials featuring this property and their potential for device applications have been less explored. We find that in these systems, the spin-polarization of edge states can be controlled with an external electric field breaking the mirror symmetry. This symmetry requires that the spin-polarization is perpendicular to the mirror plane, therefore, the electric field induces spin-polarization components parallel to the mirror plane. Since this field preserves the TR topological protection, we propose a transistor model using the spin-direction of protected edge states as a switch. In order to illustrate the generality of the proposed phenomena, we consider compounds protected by mirror planes parallel and perpendicular to the structure, e.g., Na$_3$Bi and half-functionalized (HF) hexagonal compounds, respectively. For this purpose, we first construct a tight-binding effective model for the Na$_3$Bi compound and predict that HF-honeycomb lattice materials are also dual topological insulators.