Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions

E. Abrahams; P. W. Anderson; D. C. Licciardello; T. V. Ramakrishnan

doi:10.1103/PhysRevLett.42.673

Milestone

Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions

E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan

Phys. Rev. Lett. 42, 673 – Published 5 March 1979

An article within the collection: Letters from the Past - A PRL Retrospective

Abstract

Arguments are presented that the $T = 0$ conductance $G$ of a disordered electronic system depends on its length scale $L$ in a universal manner. Asymptotic forms are obtained for the scaling function $β (G) = \frac{d \ln G}{d \ln L}$ , valid for both $G ≪ G_{c} ≃ \frac{e^{2}}{ℏ}$ and $G ≫ G_{c}$ . In three dimensions, $G_{c}$ is an unstable fixed point. In two dimensions, there is no true metallic behavior; the conductance crosses over smoothly from logarithmic or slower to exponential decrease with $L$ .

Received 7 December 1978

DOI:https://doi.org/10.1103/PhysRevLett.42.673

Collections

This article appears in the following collection:

Letters from the Past - A PRL Retrospective

2008 marked PRL’s 50th anniversary. As part of the celebrations a collection of milestone Letters was started. The collection contains Letters that have made long-lived contributions to physics, either by announcing significant discoveries, or by initiating new areas of research.