Localisation in topologically disordered systems

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Abstract
The authors study a one-electron tight-binding Hamiltonian with topological disorder using the novel concept of 'quantum connectivity'. The off-diagonal matrix elements are taken to be of the form J(ij)=-V0e-r(ij)a(B)/, and J(ij)=-V0(1+-4(ij)a(B)/) e-r(ij)a(B)/, where rij is the distance between the sites i and j, and the diagonal elements are all zero. In three dimensions the dimensionless parameter R=n13/aB, where n is the concentration of sites, characterises the disorder. They find that an Anderson transition takes place at Rc=0.257+or-0.010 and Rc=0.220+or-0.026 for the two models respectively. They also calculate the correlation length exponents in each case, finding v=1.95+or-0.13 and v=1.63+or-0.17 respectively. In two dimensions they do not observe an Anderson transition.