Quantum percolation in three-dimensional systems

The quantum site- and bond-percolation problems, which are defined by a disordered tight-binding Hamiltonian with a binary probability distribution, are studied using finite-size scaling methods. For the simple-cubic lattice, the dependence of the mobility edge on the strength of the disorder is obtained for both the site- and bond-percolation case. We find that the quantum percolation threshold is ${\mathit{p}}_{\mathit{q}}^{\mathit{s}}$=0.44±0.01 for the site case and ${\mathit{p}}_{\mathit{q}}^{\mathit{b}}$=0.32±0.01 for the bond case. A detailed numerical study of the density of states (DOS) is also presented. A rich structure in the DOS is obtained and its dependence on the concentration and strength of disorder is presented.