Two special cases of Anderson localisation

Abstract

Two special cases of Anderson localisation which are considered relatively simple are the band-centre electron with only random hopping matrix elements, and the band-edge electron with random site energies. A careful investigation of these two cases shows that the band-centre electron is localised in the sense that the wavefunction does not extend over larger and larger spaces as the system becomes large. On the other hand, the band-edge electrons do become more and more extended in large systems because the uncertainty principle limits their curvature.