  Recent years have witnessed great interest in the quantum spin Hall effect
(QSHE) which is a new quantum state of matter with nontrivial topological
property due to the scientific importance as a novel quantum state and the
technological applications in spintronics. Taking account of Si, Ge significant
importance as semiconductor material and intense interest in the realization of
QSHE for spintronics, here we investigate the spin-orbit opened energy gap and
the band topology in recently synthesized silicene using first-principles
calculations. We demonstrate that silicene with topologically nontrivial
electronic structures can realize QSHE by exploiting adiabatic continuity and
direct calculation of the Z2 topological invariant. We predict that QSHE in
silicene can be observed in an experimentally accessible low temperature regime
with the spin-orbit band gap of 1.55 meV, much higher than that of graphene due
to large spin-orbit coupling and the low-buckled structure. Furthermore, we
find that the gap will increase to 2.90 meV under certain pressure strain.
Finally, we also study germanium with similar low buckled stable structure, and
predict that SOC opens a band gap of 23.9 meV, much higher than the liquid
nitrogen temperature.
