Conductance of finite systems and scaling in localization theory
- Kapitza Institute for Physical Problems (Russian Federation)
The conductance of finite systems plays a central role in the scaling theory of localization (Abrahams et al., Phys. Rev. Lett. 42, 673 (1979)). Usually it is defined by the Landauer-type formulas, which remain open the following questions: (a) exclusion of the contact resistance in the many-channel case; (b) correspondence of the Landauer conductance with internal properties of the system; (c) relation with the diffusion coefficient D({omega}, q) of an infinite system. The answers to these questions are obtained below in the framework of two approaches: (1) self-consistent theory of localization by Vollhardt and Woelfle, and (2) quantum mechanical analysis based on the shell model. Both approaches lead to the same definition for the conductance of a finite system, closely related to the Thouless definition. In the framework of the self-consistent theory, the relations of finite-size scaling are derived and the Gell-Mann-Low functions {beta}(g) for space dimensions d = 1, 2, 3 are calculated. In contrast to the previous attempt by Vollhardt and Woelfle (1982), the metallic and localized phase are considered from the same standpoint, and the conductance of a finite system has no singularity at the critical point. In the 2D case, the expansion of {beta}(g) in 1/g coincides with results of the {sigma}-model approach on the two-loop level and depends on the renormalization scheme in higher loops; the use of dimensional regularization for transition to dimension d = 2 + {epsilon} looks incompatible with the physical essence of the problem. The results are compared with numerical and physical experiments. A situation in higher dimensions and the conditions for observation of the localization law {sigma}({omega}) {proportional_to} -i{omega} for conductivity are discussed.
- OSTI ID:
- 22069261
- Journal Information:
- Journal of Experimental and Theoretical Physics, Vol. 115, Issue 5; Other Information: Copyright (c) 2012 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA); ISSN 1063-7761
- Country of Publication:
- United States
- Language:
- English
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