Single-layer structures of a100- and b010-Gallenene: a tight-binding approach.

Using the simplified linear combination of atomic orbitals (LCAO) method in combination with ab initio calculations, we construct a tight-binding (TB) model for two different crystal structures of monolayer gallium: a100- and b010-Gallenene. The analytical expression for the Hamiltonian and numerical results for the overlap matrix elements between different orbitals of the Ga atoms and for the Slater and Koster (SK) integrals are obtained. We find that the compaction of different structures affects significantly the formation of the orbitals. The results for a100-Gallenene can be very well explained with an orthogonal basis set, while for b010-Gallenene we have to assume a non-orthogonal basis set in order to construct the TB model. Moreover, the transmission properties of nanoribbons of both monolayers oriented along the AC and ZZ directions are also investigated and it is shown that both AC- and ZZ-b010-Gallenene nanoribbons exhibit semiconducting behavior with zero transmission while those of a100-Gallenene nanoribbons are metallic.