The effects of thermal and electric fields on the electronic structures of silicene

We have investigated the effects of thermal and electric fields on the electronic properties of silicene. The effects were studied by a statistical analysis of canonical ensembles combined with the tight binding method. The tight binding parameters of silicene were obtained by fitting with the first principles results. We analysed the statistics of the gaps, the masses of the Dirac fermions and the effective speeds of light as a function of the cell dimension N. We show that the symmetry breaking caused by the buckling disorder in the thermal field alters the band structures of the silicene with small cells greatly. However, the buckling variation of any atom is compensated by other atoms in a large cell. Thus the band structure features near the Fermi energy in the pristine silicene are still protected by the sublattice symmetry in the thermal field. Moreover, the thermal field enhances the effect of the electric field to generate a band gap. The randomly buckled silicene needs a much smaller electric field than the pristine silicene. The higher temperature corresponds to a larger gap under the same electric field. All these features make silicene a better candidate for electronic devices at ambient temperature.