Low-energy bands, optical properties, and spin/valley-Hall conductivity of silicene and germanene

In this work, we study systematically low-energy bands, optical absorbance and spin/valley-Hall conductivity of silicene and germanene in the presence of a perpendicular electric field. Our analytical calculations indicate that both silicene and germanene are semiconductors with a tiny energy gap and we can control their energy gap by the perpendicular electric field. Our calculations also demonstrate that the low-frequency optical absorbance of silicene is much greater than that of germanene and the external electric field plays an important role in determining the optical absorption peaks. When the Fermi level is in the forbidden band, the Hall conductivity is quantized, while spin/valley-Hall conductivities of both silicene and germanene depend strongly on the Fermi energy when the Fermi level is in the conduction band. Analytical results for spin/valley-Hall conductivities of silicene and germanene are presented in detail in this work.