  Silicene consists of a monolayer of silicon atoms in a buckled honeycomb
structure. It was recently discovered that the symmetry of such a system allows
for interesting Rashba spin-orbit effects. A perpendicular electric field is
able to couple to the sublattice pseudospin, making it possible to electrically
tune and close the band gap. Therefore, external electric fields may generate a
topological phase transition from a topological insulator to a normal insulator
(or semimetal) and vice versa. The contribution of the present article to the
study of silicene is twofold: First, we perform a group theoretical analysis to
systematically construct the Hamiltonian in the vicinity of the $K$ points of
the Brillouin zone and discover a new, but symmetry allowed term. Subsequently,
we identify a tight binding model that corresponds to the group theoretically
derived Hamiltonian near the $K$ points. Second, we start from this tight
binding model to analyze the topological phase diagram of silicene by an
explicit calculation of the $Z_2$ topological invariant of the band structure.
To this end, we calculate the $Z_2$ topological invariant of the honeycomb
lattice in a manifestly gauge invariant way which allows us to include $S_z$
symmetry breaking terms -- like Rashba spin orbit interaction -- into the
topological analysis. Interestingly, we find that the interplay of two Rashba
terms can generate a non-trivial quantum spin Hall phase in silicene. This is
in sharp contrast to the more extensively studied honeycomb system graphene
where Rashba spin orbit interaction is known to compete with the quantum spin
Hall effect in a potentially detrimental way.

Mesoscale and Nanoscale Physics