Spin orbit coupling induced band gap in gemanene modulated by external field

We investigate the electronic band structure of germanene crystal by using the sixteen band tight-binding calculation. We focus on the modulation of its band gap with spin-orbit coupling (SOC), perpendicular electric field and magnetic field. Our calculation shows that the SOC opens a tunable band gap in the Dirac-type electronic structures, and plays a crucial rule in the formation of the energy band gap. The influence of SOC on the gap in germanene is much larger than that in graphene, which makes germanene an ideal candidate to exhibit the quantum spin Hall effect at room temperature. We also find that the electronic structure and topological property of germanene can be tuned by the external field significantly. Thus the electronic structure of germanene can be controlled to produce metallic, semiconducting, or insulating properties by applying an appropriate external field. In addition, the key features of the band structure induced by the electrical field and magnetic field are quite different. For the electric field applied, two spin-up states produce a gap at K point, in contrast, two spin-down states do it at K′ points. While for the magnetic field present, the band gaps are formed by the spin-up states from the conduction band and spin-down state from the valance band at both the K and K′ points. This modulation behavior of the band gap by the external field paves a way to the realization of germanene based spintronic devices.