Obtaining localization properties efficiently using the Kubo-Greenwood formalism

Abstract

We establish, through numerical calculations and comparisons with a recursive Green's-function based implementation of the Landauer-B\"uttiker formalism, an efficient method for studying Anderson localization in quasi-one-dimensional and two-dimensional systems using the Kubo-Greenwood formalism. Although the recursive Green's-function method can be used to obtain the localization length of a mesoscopic conductor, it is numerically very expensive for systems that contain a large number of atoms transverse to the transport direction. On the other hand, linear scaling has been achieved with the Kubo-Greenwood method, enabling the study of effectively two-dimensional systems. While the propagating length of the charge carriers will eventually saturate to a finite value in the localized regime, the conductances given by the Kubo-Greenwood method and the recursive Green's-function method agree before the saturation. The converged value of the propagating length is found to be directly proportional to the localization length obtained from the exponential decay of the conductance.