Anomalous transport: results, conjectures and applications to quasicrystals

Bellissard, Jean

doi:10.1016/s0921-5093(00)01129-1

Cited by 13 publications

(4 citation statements)

References 36 publications

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“…At low temperature, all samples are disordered-like (long length scales) and the interpretation of section 4.1 remains valid. In the intermediate temperature, the more disordered ribbons (of lesser resistivity) become disordered-like, but the high resistive ribbons (more ordered) could still be in the non-disordered QC regime: the power law dependence observed from 10 up to 100 K for ribbons around R 100 would then be attributed to QC laws like equation ( 9), as has been suggested by some authors [46,47]. However, such a description relies on speculative assumptions in i-AlPdRe like the change of L el with R and T QC values below 300 K.…”

Section: Quasicrystalline Specificity?mentioning

confidence: 61%

Thouless and critical regimes in insulating icosahedral AlPdRe ribbons

Delahaye¹,

Berger²,

Fourcaudot³

2003

J. Phys.: Condens. Matter

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We present conductivity measurements of quasicrystalline AlPdRe ribbons in a wide range of temperature (20 mK–300 K), for icosahedral samples spanning a broad resistivity range (R = ρ4 K/ρ300 K from 2 to 209). We focus here on a detailed analysis of the temperature dependence of the conductivity σ(T) for the insulating samples (R>16). Three successive regimes are revealed as the temperature is increased to 300 K: a low temperature variable range hopping-like behaviour, followed by a Thouless regime and a high temperature critical regime. The temperature dependence of the inelastic scattering time found elsewhere by magnetoresistance data analysis accounts well for the change of curvature in σ(T) and the trends observed as R varies. The present results point to a similar behaviour between quasicrystalline AlPdRe samples and disordered systems close to the metal–insulator transition, in accordance with our previous analysis of the very low temperature insulating regime and of the finding of conductivity scaling laws.

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Section: Quasicrystalline Specificity?mentioning

confidence: 61%

Thouless and critical regimes in insulating icosahedral AlPdRe ribbons

Delahaye¹,

Berger²,

Fourcaudot³

2003

J. Phys.: Condens. Matter

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“…The theoretical prediction that critical electronic states decaying as a power law given by ϰr Ϫ␤ should lead to a conductivity dependence of the form ϰT 2␤/d , where d is the dimensionality of the system, [52][53][54][55] has been invoked to justify power-law fittings. Variable range hopping conduction between strongly localized states, related to a self-similar hierarchical nesting of atomic clusters, 56 or a multiple-valley fractional Fermi-surface model for the electronic structure of QC's [57][58][59] have been also considered to explain the anomalous transport properties.…”

Section: ͑T ͒ϭ͑ 0 ͒ϩ⌬͑ T ͒ ͑1͒mentioning

confidence: 99%

Universal features in the electrical conductivity of icosahedral Al-transition-metal quasicrystals

Maciá

2002

Phys. Rev. B

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In this work we report the existence of certain universal features in the temperature dependence of the electrical conductivity of Al-transition-metal icosahedral quasicrystals, extending the results previously reported on the inverse Matthiessen rule ͓D. Mayou, C. Berger, F. Cyrot-Lackmann, T. Klein, and P. Lanco, Phys. Rev. Lett. 70, 3915 ͑1993͔͒. We propose a tentative classification scheme providing a unified description of the electrical conductivity curves over a broad temperature range. We introduce a phenomenological model describing the electrical conductivity of icosahedral quasicrystals, deriving closed analytical expressions. We compare our analytical results with suitable experimental data and illustrate the use of the introduced phenomenological coefficient in order to extract information about the electronic structure of the samples from a fitting analysis of the experimental conductivity curves.

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“…Section 4 reviews the basics of the noncommutative theory of electron transport and gives the derivation of the noncommutative Kubo formula. In both Section 3 and Section 4 we follow closely the work of Bellissard, Schulz-Baldes and their collaborators [6,53,54,4,61,7,5].…”

Section: Introductionmentioning

confidence: 99%

“…The purpose of this work is to demonstrate that the noncommutative Kubo formula [6,53,54,4,61,7,5,12] for the transport coefficients of aperiodic solids in magnetic fields can be efficiently evaluated on a computer. Our main message is that the noncommutative Kubo formula, which is now well known for its pivotal role in the theoretical foundation of charge transport in aperiodic systems [53,3,4,8,7,5,40], can also provide an effective numerical solution to the difficult problem of computing the transport coefficients for realistic quantum models of aperiodic systems. For disordered quantum lattice systems in magnetic fields, we derive a "canonical" finite-volume approximation to the noncommutative Kubo formula that can be efficiently evaluated on a computer.…”

Section: Introductionmentioning

confidence: 99%

Quantum Transport in Disordered Systems Under Magnetic Fields: A Study Based on Operator Algebras

Prodan

2012

Applied Mathematics Research eXpress

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The linear conductivity tensor for generic homogeneous, microscopic quantum models was formulated as a noncommutative Kubo formula in Refs. [6,53,54]. This formula was derived directly in the thermodynamic limit, within the framework of C * -algebras and noncommutative calculi defined over infinite spaces. As such, the numerical implementation of the formalism encountered fundamental obstacles. The present work defines a C * -algebra and an approximate noncommutative calculus over a finite real-space torus, which naturally leads to an approximate finite-volume noncommutative Kubo formula, amenable on a computer. For finite temperatures and dissipation, it is shown that this approximate formula converges exponentially fast to its thermodynamic limit, which is the exact noncommutative Kubo formula. The approximate noncommutative Kubo formula is then deconstructed to a form that is implementable on a computer and simulations of the quantum transport in a 2-dimensional disordered lattice gas in a magnetic field are presented.

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Anomalous transport: results, conjectures and applications to quasicrystals

Cited by 13 publications

References 36 publications

Thouless and critical regimes in insulating icosahedral AlPdRe ribbons

Thouless and critical regimes in insulating icosahedral AlPdRe ribbons

Universal features in the electrical conductivity of icosahedral Al-transition-metal quasicrystals

Quantum Transport in Disordered Systems Under Magnetic Fields: A Study Based on Operator Algebras

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