Fig. 1. (Color online) Buckled honeycomb lattice of germanene.

Fig. 2. (Color online) Schematic diagram of the band structure of germanene near the K and K^’ points of the surface Brillouin zone. From left to right: band structure without a spin-orbit gap, with a spin-orbit gap, applied electric field smaller than the critical value, applied electric field equal to the critical value and applied electric field larger than the critical value. Red and green refer to spin up and spin down bands, respectively.