We present first-principles calculations of silicene/graphene and germanene/graphene bilayers. Various supercell models are constructed in the calculations in order to reduce the strain of the lattice-mismatched bilayer systems. Our energetics analys
is and electronic structure results suggest that graphene can be used as a substrate to synthesize monolayer silicene and germanene. Multiple phases of single crystalline silicene and germanene with different orientations relative to the substrate could coexist at room temperature. The weak interaction between the overlayer and the substrate preserves the low-buckled structure of silicene and germanene, as well as their linear energy bands. The gap induced by breaking the sublattice symmetry in silicene on graphene can be up to 57 meV.
By viewing the electron as a wavepacket in the positive energy spectrum of the Dirac equation, we are able to achieve a much clearer understanding of its behavior under weak electromagnetic fields. The intrinsic spin magnetic moment is found to be es
tablished from the self-rotation of the wavepacket. A non-canonical structure is also exhibited in the equations of motion due to non- Abelian geometric phases of the Dirac spinors. The wavepacket energy can be expressed simply in terms of the kinetic, electrostatic, and Zeeman terms only. This can be transformed into an effective quantum Hamiltonian by a novel scheme, and reproduces the Pauli Hamiltonian with all-order relativistic corrections.
