Anderson localization in topologically disordered systems

A self-consistent theory of localization in a tight-binding model of topologically disordered systems is investigated. A key element of the theory is use of a disordered reference system in which the structure of the medium is taken into account. The spatial disorder inherent in the Boltzmann center-of-mass distribution is taken as the explicit source of lateral disorder, and the effects of simultaneous site-diagonal disorder are also included. The theory is formulated in a manner which circumvents use of the so-called upper-limit approximation. The Anderson transition density predicted by the theory is estimated for transfer-matrix elements of the forms V(R)∼$R^{\mathrm{-}n}$, V(R)∼exp(-R/$a_H$), and V(R)∼(1+R/$a_H$)exp(-R/$a_H$). Full mobility-edge trajectories for power-law transfer-matrix elements are also determined, with particular emphasis on the cases n=3 and 5 corresponding, respectively, to dipolar and quadrupolar excitons. A connection is also made between the density of states determined from the self-consistent theory and that resultant from solution of the quantum mean spherical integral equation.