Silicene beyond mono-layers--different stacking configurations and their properties.

We carry out a computational study on the geometric and electronic properties of multi-layers of silicene in different stacking configurations using state-of-the-art ab initio density functional theory based calculations. In this work we investigate the evolution of these properties with increasing number of layers (n) ranging from 1 to 10. Although a mono-layer of silicene possesses properties similar to those of graphene, our results show that the geometric and electronic properties of multi-layers of silicene are strikingly different from those of multi-layers of graphene. We observe that strong inter-layer covalent bonding exists between the layers in multi-layers of silicene as opposed to weak van der Waals bonding which exists between the graphene layers. The inter-layer bonding strongly influences the geometric and electronic structures of these multi-layers. Like bi-layers of graphene, silicene with two different stacking configurations AA and AB exhibits linear and parabolic dispersions around the Fermi level, respectively. However, unlike graphene, for bi-layers of silicene, these dispersion curves are shifted in the band diagram; this is due to the strong inter-layer bonding present in the latter. For n > 3, we study the geometric and electronic properties of multi-layers with four different stacking configurations, namely AAAA, AABB, ABAB and ABC. Our results on cohesive energy show that all the multi-layers considered are energetically stable. Furthermore, we find that the three stacking configurations (AAAA, AABB and ABC) containing tetrahedral coordination have much higher cohesive energy than the Bernal (ABAB) stacking configuration. This is in contrast to the case of multi-layers of graphene, where ABAB is reported to be the lowest energy configuration. We also observe that bands near the Fermi level in lower energy stacking configurations AAAA, AABB and ABC correspond to the surface atoms and these surface states are responsible for the semi-metallic character of these multi-layers.