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Phys. Rev. Lett. 42, 673–676 (1979)

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

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E. Abrahams
Serin Physics Laboratory, Rutgers University, Piscataway, New Jersey 08854

P. W. Anderson*, D. C. Licciardello, and T. V. Ramakrishnan†
Joseph Henry Laboratories of Physics, Princeton University, Princeton, New Jersey 08540

Received 7 December 1978; published in the issue dated 5 March 1979

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)=dlnG/dlnL, valid for both G≪Gc≃e2/ℏ and G≫Gc. In three dimensions, Gc 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.

© 1979 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevLett.42.673
DOI:
10.1103/PhysRevLett.42.673

*Also at Bell Laboratories, Murray Hill, N. J. 07974.

†On leave from Indian Institute of Technology, Kanpur, India.

 
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