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

1979/03/05 by Elihu Abrahams, Philip W. Anderson, D. C. Licciardello +1 · 120 citations
Physics and Astronomy · #Quantum and electron transport phenomena #Theoretical and Computational Physics #Surface and Thin Film Phenomena

paper · doi:10.1103/physrevlett.42.673

openalex publication_date 1979/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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 \ensuremathβ(G)=(dlnG)/(dlnL), valid for both G\ensuremath≪G_c\ensuremath≃\frace²\ensuremathℏ and G\ensuremath≫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.

Citations

• Numerical studies of localization in disordered systems
• Electrons in disordered systems and the theory of localization

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