On the spatial structure of anomalously localised states in disordered conductors

TL;DR

This paper investigates the spatial structure of highly localized wave functions in disordered conductors, comparing quasi-one-dimensional and three-dimensional samples to understand differences in their background intensities.

Contribution

It provides a detailed analysis of the spatial profiles of anomalously localized states in different dimensions within the Anderson model, highlighting dimensional differences.

Findings

In 3D, background intensity is constant and independent of distance.

In quasi-1D, background intensity redistributes towards the localization center.

Results agree with theoretical predictions for quasi-1D states.

Abstract

We study the spatial structure of wave functions with exceptionally high local amplitudes in the Anderson model of localisation. By means of exact diagonalisations of finite systems, we obtain and analyse images of these wave functions: we compare the spatial structure of such anomalously localised states in quasi-one-dimensional samples to that in three-dimensional samples. In both cases the average wave-function intensity exhibits a very narrow peak. The background intensity, however, is found to be very different in these two cases: in three dimensions, it is constant, independent of the distance to the localisation centre (as expected for extended states). In quasi-one dimensional samples, on the other hand, it is redistributed towards the localisation centre and approaches a characteristic form predicted in [A. D. Mirlin, Phys. Rep. 326, 249 (2000)].