Quantum spin Hall effect in silicene and two-dimensional germanium

We investigate the spin-orbit opened energy gap and the band topology in recently synthesized silicene as well as two-dimensional low-buckled honeycomb structures of germanium using first-principles calculations. We demonstrate that silicene with topologically nontrivial electronic structures can realize the quantum spin Hall effect (QSHE) by exploiting adiabatic continuity and the direct calculation of the Z₂ topological invariant. We predict that the QSHE can be observed in an experimentally accessible low temperature regime in silicene with the spin-orbit band gap of 1.55 meV, much higher than that of graphene. Furthermore, we find that the gap will increase to 2.9 meV under certain pressure strain. Finally, we also study germanium with a similar low-buckled stable structure, and predict that spin-orbit coupling opens a band gap of 23.9 meV, much higher than the liquid nitrogen temperature.