  Bilayer silicene has richer physical properties than bilayer graphene due to
its buckled structure together with its trigonal symmetric structure. The
buckled structure arises from a large ionic radius of silicon, and the trigonal
symmetry from a particular way of hopping between two silicenes. It is a
topologically trivial insulator since it carries a trivial $\mathbb{Z}_{2}$
topological charge. Nevertheless, its physical properties are more akin to
those of a topological insulator than those of a band insulator. Indeed, a
bilayer silicene nanoribbon has edge modes which are almost gapless and
helical. We may call it a quasi-topological insulator. An important observation
is that the band structure is controllable by applying the electric field to a
bilayer silicene sheet. We investigate the energy spectrum of bilayer silicene
under electric field. Just as monolayer silicene undergoes a phase transition
from a topological insulator to a band insulator at a certain electric field,
bilayer silicene makes a transition from a quasi-topological insulator to a
band insulator beyond a certain critical field. Bilayer silicene is a metal
while monolayer silicene is a semimetal at the critical field. Furthermore we
find that there are several critical electric fields where the gap closes due
to the trigonal warping effect in bilayer silicene.

Mesoscale and Nanoscale Physics;Materials Science