Localization in quantum percolation: Transfer-matrix calculations in three dimensions

Abstract

The quantum site percolation problem, which is defined by a disordered tight-binding Hamiltonian with a binary probability distribution, is studied using finite-size scaling methods. For the simple cubic lattice, the dependence of the mobility edge on the strength of the site energy is obtained. Exactly at the center of each subband the states appear to be always localized. The lowest value of the quantum site percolation threshold is $p_q$=0.44±0.01 and occurs for an energy near the center of the subband. These numerical results are found to be in satisfactory agreement with the predictions of the potential-well analogy, based on a cluster coherent-potential approximation. The integrated density of states is also calculated numerically. A spike in the density of states exactly at the center of the subband and a gap around it are observed, in agreement with earlier work by Kirkpatrick and Eggarter.