Surface Structure and Surface State of a Tight-Binding Model on a Diamond Lattice

Abstract: Surface states of a tight-binding model with nearest-neighbor hopping on a diamond lattice of finite thickness are investigated. We consider systems with (001), (110), and (111) surfaces. Even if the surface direction is fixed, there is freedom to choose the surface structure due to the two-sublattice nature of a diamond lattice. The existence of surface states is governed by the topology of the matrix elements of the bulk Hamiltonian. In this sense, the existence of surface states is determined by the bulk Hamiltonian. However, the matrix elements depend on the choice of the unit cell, which should be chosen to conform to the surface structure. Thus, the surface states depend on the surface structure. We find that for each surface direction, there are two choices of surface structure, and depending on the chosen structure, the corresponding surface states emerge in distinct regions of the surface Brillouin zone.