Dimension-enriched essential properties of Ge-related materials

The dimensionality of materials could determine active physical and chemical environments which consist of finite-width confinement. The close relations of crystal structures among nanoribbons, nanotubes, and monolayers have been utilized to synthesize specific low-dimensional materials. In this chapter, through the theoretical framework implemented in VASP, the essential properties of 1D germanene nanoribbons were explored, exhibiting the finite quantum confinement effects, open edge structures, and buckled honeycomb crystal. Especially, 1D germanene nanoribbons with specific widths and open edge structures indicate the diversified quasiparticle phenomena, which are totally different from 2D and 3D allotropes. In this system, the dangling bonds at boundaries/the hydrogen decorations, the significant sp3 bondings, the non-perpendicular π and σ bondings, and the spin-orbital interactions are investigated, which perform the highly non-uniform environments corresponding to the geometry-enriched fundamental properties. All systems belong to the middle-, or narrow-gap semiconductors, in which the bandgap magnitudes gradually decline in the increment of ribbon width. Moreover, armchair structures could be divided into three categories where the dimer line number NA=3I+2 reveal the smallest direct gaps. Importantly, a lot of van Hove singularities induced by the band-edge states of 1D energy sub-bands, show the crucial features of 4pz-, (4s, 4px, 4py)- and (4s, 4px, 4py, 4pz) within the different energy ranges.