Monolayer and bilayer germanene systems

In this chapter show that the geometric and electronic properties of germanene-related system have diversified phenomena. Critical factors of group-IV monoelements, like buckled/planar structures, stacking configurations, layer numbers, and van der Waals interactions of bilayer composites, are considered simultaneously. The theoretical framework developed provides a concise physical and chemical picture. Delicate evaluations and analyses have been made on the optimal lattices, energy bands, and orbital-projected van Hove singularities. They provide decisive mechanisms, such as buckled/planar honeycomb lattices, multi-/single-orbital hybridizations, and significant/negligible spin–orbital couplings. We investigate the stacking-configuration-induced dramatic transformations of essential properties by relative shift in bilayer graphenes and silicenes. The lattice constant, interlayer distance, buckling height, and total energy essentially depend on the magnitude and direction of the relative shift: AA and AB. Apparently, bilayer systems are quite different from monolayer germanene in terms of geometric structures, electronic properties, orbital hybridizations, interlayer hopping integrals, and spin interactions.