Numerical Investigations of Scaling at the Anderson Transition

Abstract

At low temperature T, a significant difference between the behavior of crystals on the one hand and disordered solids on the other is seen: sufficiently strong disorder can give rise to a transition of the transport properties from conducting behavior with finite resistance R to insulating behavior with R=∞ as T→0 as was pointed out by Anderson in 1958 [4]. This phenomenon is called the disorder-driven metal-insulator transition (MIT) [3, 1, 4] and it is characteristic to non-crystalline solids. The mechanism underlying this MIT was attributed by Anderson not to be due to a finite gap in the energy spectrum which is responsible for an MIT in band gap or Mott insulators [5]. Rather, he argued that the disorder will lead to interference of the electronic wave function ψ(x) with itself such that it is no longer extended over the whole solid but is instead confined to a small part of the solid. This localization effect excludes the possibility of diffusion at T=0 and thus the system is an insulator.