Germanene, one of the most important two-dimensional materials after graphene and silicone have been discovered, is attracting wide attentions due to its many excellent physical properties. Since a suitable band gap is needed for the electronics and optoelectronics, the lack of a band gap has essentially restricted the practical applications of germanene in macroelectronics. In this article, density functional theory calculations with van de Waals corrections is utilized to study the geometric and electronic properties of germanene (Ge), germanane (GeH) and germanene/germanane (Ge/GeH) bilayer. The band gaps for Ge and GeH are zero and 1.16 eV, respectively. For the Ge/GeH bilayer, a considerable binding energy of 273 meV/unit cell is obtained between Ge and GeH layers. This value is smaller than that of Ge bilayer (402 meV/unit cell), but larger than that of GeH bilayer (211 meV/unit cell), indicating a considerable GeH/ bonding. This means that Ge and GeH layers could be combined steadily by the interlayer weak interactions. Meanwhile, a band gap of 85 meV is opened, which is contributed to the breaking of the equivalence of the two sublattices in the Ge sheet, yielding a nonzero band gap at the K point. Charge density difference indicates that the electrons on the s orbital of H transfer to the Ge_p orbital, enhancing the interlayer interactions. It should be noted here that the van de Waals corrections are pretty important for the geometric and electronic properties of the Ge/GeH bilayer. Without the van de Waals corrections, the binding energy of the Ge/GeH bilayer is reduced from 273 meV/unit cell to only 187 meV/unit cell, severely underestimated the strength of the weak forces between Ge and GeH layers, resulting in a much smaller band gap of 50 meV. Interestingly, no band gap is obtained for the sandwich structure GeH/Ge/GeH, in which the equivalence of two sublattices in germanene is kept. Finally, all the results are confirmed by the high accurate hybrid functional calculations. At the Heyd-Scuseria-Ernzerhof level, the band gap of Ge/GeH bilayer is 117 meV, slightly larger than 85 meV at the Perder-Burke-Ernzerhof level. Our work would promote utilizing germanene in microelectronics and call for more efforts in using weak interactions for band structure engineering.
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