Anisotropic tight-binding model for localization

The anisotropic tight-binding model, which is defined by a disordered tight-binding Hamiltonian with a transfer-energy-matrix element in the z direction, t, different than the one in the x-y plane is studied using finite-size scaling methods. The dependence of the mobility edge on the strength of anisotropy t (0{≤}t{≤}1) is obtained for the center of the band, E=0. Even for very low-t values an appreciable amount of disorder is needed to localize the E=0 state. These results are found to be in satisfactory agreement with the predictions of the potential-well analogy, coupled with the coherent-potential approximation.