A comparative first-principles study of orbital hybridization in two-dimensional C, Si, and Ge

Information on orbital hybridization is very important to understand the structural, physical, and chemical properties of a material. Results of a comparative first-principles study on the behaviours of orbital hybridization in the two-dimensional single-element phases by carbon, silicon, and germanium are presented. From the well-known three-dimensional hexagonal lonsdaleite structure, in which the atoms are in ideal sp(3)-bonding, the layer spacing along c-axis is gradually stretched to simulate the evolutions of structural and electronic properties from three-dimensional to two-dimensional lattice configurations in the three materials. A turning point of the total system energy due to the sp(3) to sp(2) transition is observed during this process in carbon. In contrast, no such phenomenon is found in silicon and germanium. The differences in electronic structure and bonding behaviour are further examined through comparative investigation of atomic angular-momentum projected density of states and electronic energy band spectrums of these materials. We demonstrate that the valence electronic orbital in the two-dimensional hexagonal crystals of Si and Ge shows sp(3)-like behaviour for the partial hybridization of s and p(z), which leads to their different lattice configurations to graphene. The role of π-bonds in stabilizing the flat configuration of graphene is also discussed.