The quantum valley Hall effect in twisted bilayer silicene and germanene

We show that twisted bilayers of silicene or germanene can be utilized for a novel transistor concept that relies on the quantum valley Hall effect. The application of an electric field normal to the twisted bilayer allows to tailor the size of the bandgap in AB- and BA-stacked domains of the twisted bilayer. In contrast to twisted bilayer graphene, the AB and BA bandgaps in twisted bilayer silicene and germanene are not inverted for small electric fields. However, above a critical electric field, the bandgaps invert, giving rise to a two-dimensional triangular network of topologically protected channels. The possibility to controllably switch these topologically protected states on and off using an electric field, combined with its inherent robustness against defects and impurities, establishes a foundation for a new type of transistor with an exceptional resilience.