Scaling properties near the Anderson transition

Efetov, K. B.; Viehweger, O.

doi:10.1103/physrevb.45.11546

Cited by 31 publications

(34 citation statements)

References 14 publications

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“…For the special case of noninteracting disordered electrons some progress has been made by studying the localization transition on a Bethe lattice (Efetov, 1984(Efetov, , 1987Zirnbauer, 1986) or in an ensemble of sparse matrices (Fyodorov and Mirlin, 1991). Similar results are obtained by treating the graded or supersymmetric nonlinear sigma model in an effective-medium approximation (Efetov, 1988;Efetov and Viehweger, 1992). The resulting phase transition is rather different from the one expected on the basis of either the c = d -2 expansion approach or threedimensional computer simulations.…”

Section: B Symmetry Considerations and Renormaiizabilitymentioning

confidence: 86%

The Anderson-Mott transition

1994

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The interacting disordered electron problem is reviewed with emphasis on the quantum phase transitions that occur in a model system and on the field-theoretic methods used to describe them. An elementary discussion of conservation laws and diffusive dynamics is followed by a detai1ed derivation of the extended nonlinear sigma model, which serves as an effective field theory for the problem. A general scaling theory of metal-insulator and related transitions is developed, and explicit renormalization-group calculations for the various universality classes are reviewed and compared with experimental results. A discussion of pertinent physical ideas and phenomenological approaches to the metal-insulator transition not contained in the sigma-model approach is given, and phase-transition aspects of related problems, like disordered superconductors and the quantum Hall effect, are discussed. The review concludes with a list of open problems.

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Section: B Symmetry Considerations and Renormaiizabilitymentioning

confidence: 86%

The Anderson-Mott transition

1994

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“…Thus, the critical concentration of the links p c corresponds again to the case when the energy separation between the interacting states A/ra becomes comparable with their overlap J. This transition resembles for weak coupling the MI transition on the Bethe lattice [13][14][15] with the coordination number ra » 1.…”

confidence: 89%

“…(13), (15), and (20) one can see that the magnetic field shifts the transition to a lower concentration of the cross-links. Due to a random orientation of wires with respect to the field direction the region of the crossover between these two limits is very broad,…”

confidence: 91%

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Localization transition in a random network of metallic wires: A model for highly conducting polymers

Prigodin

Efetov

1993

Phys. Rev. Lett.

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We consider the Anderson metal-insulator transition in a network of randomly coupled metallic wires, which is suggested to describe transport properties of highly conducting fibril-form polymers. The absence of closed paths in the model enables us to study the transition exactly. The critical concentration of the cross-links determining the transition depends on the localization length of a single wire and on the interwire coupling. Application of a magnetic field extends the area of the metallic phase.PACS numbers: 71.20.Hk, 71.30.+h, 72.15.Rn Recently, conjugated polymers such as polyacetylene, polyaniline, and polypyrrole have attracted considerable interest in applied and fundamental research [1,2]. Their common exciting feature is that the conductivity can be increased by a few orders of magnitude upon doping. In heavily doped Tsukamoto polyacetylene the roomtemperature conductivity (CTRT) has already reached that of Cu. However, in spite of the large CTRT, transport properties of these conducting polymers are still far from being traditionally metallic.First of all, in contrast to metals, the conductivity of the polymers decreases with lowering the temperature. Depending on CTRT (i.e., on the level of doping and the degree of disorder) this decay varies from an activation-type behavior to a weak logarithmic one. For the most highly conducting samples the conductivity even approaches a residual value at low temperatures [2][3][4]. At the same time their thermoelectric power and Pauli susceptibility suggest a metallic density of states at the Fermi level in the whole temperature interval. It is noteworthy also that at low temperatures there is a significant magnetoresistance [3,4] and its sign correlates with the above temperature dependence of conductivity, being negative for highly conducting samples.On the basis of these observations it was suggested [3-6] that the highly conducting polymers are close to a metal-insulator (MI) transition driven by disorder. Since their CTRT greatly exceeds those of all known systems near the MI boundary, one can conclude also that the highly conducting polymers exhibit a new type of localizationdelocalization transition.For a physical explanation of the unusual transport properties of the polymers their chain nature seems to be very important. Electrons move primarily along polymer chains over large distances without scattering, hopping sometimes between neighboring chains. Therefore, existing theoretical considerations were based on models of either highly anisotropic dirty metals [4,7], or a quasione-dimensional system of weakly coupled chains [3,8]. The direct application of these results to polyacetylene requires a very high anisotropy of the conductivities [4,9]. However, this basic assumption of high anisotropy, based on a regular arrangement of chains, is violated in the polymers.It is common knowledge that the polymers represent a very irregular structure of interacting chains, whose description and classification are a subject of current studies [10]. The most ...

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“…1 is actually representative of a number of other threshold phenomena in condensed systems. Examples include the electrical transport of chargedensity-waves (CDWs) [2][3][4][5] and driven flux motion in type-II superconductors [6]. A basic theoretical question in all these cases is whether one can calculate the v-F curve using a suitable model, which to a large extent involves an estimate for F c and a theory for the singular behavior around the transition.…”

Section: Introductionmentioning

confidence: 99%

Driven interface depinning in a disordered medium

et al. 1997

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Abstract. The dynamics of a driven interface in a medium with random pinning forces is analyzed. The interface undergoes a depinning transition where the order parameter is the interface velocity v, which increases as v N ( F -F,)' for driving forces F close to its threshold value F,. We consider a Langevin-type Eq. which is expected to be valid close to the depinning transition of an interface in a statistically isotropic medium. By a functional renormalization group scheme the critical expo- Here, we present details of the perturbative calculation and of the derivation of the functional flow Eq. for the random-force correlator. The fixed point function of the correlator has a cusp singularity which is related to a finite value of the threshold F,, similar to the mean field theory. We also present extensive numerical simulations and compare them with our analytical results for the critical exponents. For E = I the numerical and analytical results deviate from each other by only a few percent. The deviations in lower dimensions E = 2,3 are larger and suggest that the roughness exponent is somewhat larger than the value [ = ~/ 3 of an interface in thermal equilibrium.

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Scaling properties near the Anderson transition

Cited by 31 publications

References 14 publications

The Anderson-Mott transition

The Anderson-Mott transition

Localization transition in a random network of metallic wires: A model for highly conducting polymers

Driven interface depinning in a disordered medium

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