Numéro
J. Phys. Colloques
Volume 42, Numéro C4, Octobre 1981
Proceedings of the Ninth International Conference on Amorphous and Liquid Semiconductors
Page(s) C4-37 - C4-45
DOI https://doi.org/10.1051/jphyscol:1981405
Proceedings of the Ninth International Conference on Amorphous and Liquid Semiconductors

J. Phys. Colloques 42 (1981) C4-37-C4-45

DOI: 10.1051/jphyscol:1981405

FINITE SIZE SCALING APPROACH TO ANDERSON LOCALIZATION

J.L. Pichard and G. Sarma

Service de Physique du Solide et de Résonance Magnétique, CEN-Saclay, B.P. N° 2, 91190 Gif-sur-Yvette, France


Abstract
The Anderson localization problem is studied by a new scaling theory of finite systems which has been proved to be powerful for different phase transition problems [1]. In three dimensions, there is a transition at a critical value Wc of the disorder parameter from a region of exponentially localized states to a region of extended states. When W decreases to Wc, we find a value equal to 0.66 for the critical exponent ν lative to the divergence of the localization length. In two dimensions, a critical value Wc of the disorder parameter separates a region of exponentially localized states (W > Wc) from a region of "quasi extended" states which are non square summable and fall off as R-η(W). We give the variation of the exponent η(W) in the whole "quasi extended" region. On the other hand, we show that the divergence of the localization length when W decreases to Wc is now controlled by an essential singularity. The behaviour of the dimensionless conductance is given in all the cases. In particular, in the two dimensional weak disorder phase, it is shown to obey a power law decay (L/λ)-2η(W) versus the "size" L.