Scaling Theory of Localization: Absence of Quantum Diffusion in Two Dimensions
Elihu AbrahamsSerin Physics Laboratory, Rutgers University, Piscataway, New Jersey 08854Philip W. AndersonSerin Physics Laboratory, Rutgers University, Piscataway, New Jersey 08854D. C. LicciardelloSerin Physics Laboratory, Rutgers University, Piscataway, New Jersey 08854T. V. RamakrishnanSerin Physics Laboratory, Rutgers University, Piscataway, New Jersey 08854
1979en
ABI
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 $\ensuremath{\beta}(G)=\frac{d\mathrm{ln}G}{d\mathrm{ln}L}$, valid for both $G\ensuremath{\ll}{G}_{c}\ensuremath{\simeq}\frac{{e}^{2}}{\ensuremath{\hbar}}$ and $G\ensuremath{\gg}{G}_{c}$. 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 $L$.
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