Structural stability and energy-gap modulation through atomic protrusion in freestanding bilayer silicene

We report on first-principles total-energy and phonon calculations that clarify structural stability and electronic properties of freestanding bilayer silicene. By extensive structural exploration, we reach all the stable structures reported before and find four new dynamically stable structures, including the structure with the largest cohesive energy. We find that atomic protrusion from the layer is the principal relaxation pattern which stabilizes bilayer silicene and determines the lateral periodicity. The hybrid-functional calculation shows that the most stable bilayer silicene is a semiconductor with the energy gap of 1.3 eV.