Evolution of the linear band dispersion of monolayer and bilayer germanene on Cu(111)

The structural and electronic properties of germanene are always strongly modulated by the hybridization effects with metal substrates. In order to see what will happen when a buffer layer is introduced in-between germanene and metal substrates, we study the structural and electronic properties of the recently synthesized monolayer and bilayer germanene on Cu(111) though first-principles calculations. Our results show that the monolayer germanene on Cu(111) displays a nearly flat configuration and interface states form between the Ge p_z and Cu sp-like states, with the Ge π states maintaining the Dirac character. For bilayer germanene on Cu(111), interactions with Cu(111) are reduced due to germanene inter-layer interactions, which is beneficial for the transfer of germanene. In comparison with the bottom germanene layer, the Ge p_z character of the upper germanene layer can be maintained near the Fermi level. Since the linear band dispersion is at the heart of the novel quantum phenomenon, our results will facilitate research into the synthesis, extraordinary quantum properties, and applications based on the two-dimensional (2D) germanium system.