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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 fordevice applications have been less explored. We find that in these systems, thespin-polarization of edge states can be controlled with an external electricfield breaking the mirror symmetry. This symmetry requires that thespin-polarization is perpendicular to the mirror plane, therefore, the electricfield induces spin-polarization components parallel to the mirror plane. Sincethis field preserves the TR topological protection, we propose a transistormodel using the spin-direction of protected edge states as a switch. In orderto illustrate the generality of the proposed phenomena, we consider compoundsprotected by mirror planes parallel and perpendicular to the structure, e.g.,Na$_3$Bi and half-functionalized (HF) hexagonal compounds, respectively. Forthis purpose, we first construct a tight-binding effective model for theNa$_3$Bi compound and predict that HF-honeycomb lattice materials are also dualtopological insulators.

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