Group theoretical and topological analysis of the quantum spin Hall effect in silicene
Abstract
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 spinorbit 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 paper to the study of silicene is twofold. Firstly, we perform a group theoretical analysis to systematically construct the Hamiltonian in the vicinity of the K points of the Brillouin zone and find an additional, electric field induced spinorbit term, that is allowed by symmetry. Subsequently, we identify a tightbinding model that corresponds to the group theoretically derived Hamiltonian near the K points. Secondly, we start from this tightbinding 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 spinorbit interaction—into the topological analysis. Interestingly, we find that the interplay of a Rashba and an intrinsic spinorbit term can generate a nontrivial quantum spin Hall phase in silicene. This is in sharp contrast to the more extensively studied honeycomb system graphene where Rashba spinorbit interaction is known to compete with the quantum spin Hall effect in a detrimental way.
 Publication:

New Journal of Physics
 Pub Date:
 August 2013
 DOI:
 10.1088/13672630/15/8/085030
 arXiv:
 arXiv:1305.0766
 Bibcode:
 2013NJPh...15h5030G
 Keywords:

 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 24 pages, 6 figures