Hot-Electron Effects in Two-Dimensional Hopping with a Large Localization Length

Gershenson, M. E.; Khavin, Yu. B.; Reuter, D.; Schafmeister, P.; Wieck, A. D.

doi:10.1103/physrevlett.85.1718

Cited by 39 publications

(64 citation statements)

References 27 publications

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“…A similar hopping exponent has been reported by other authors [5,10,13,14], but has rarely been discussed per se. Since there is no theory which predicts this value of the hopping exponent, its origin has been left an open question.…”

Section: Introductionsupporting

confidence: 55%

Anomalous hopping exponents of ultrathin metal films

et al. 2000

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The temperature dependence of the resistance R(T ) of ultrathin quench-condensed films of Ag, Bi, Pb and Pd has been investigated. In the most resistive films films, R(T ) = R0 exp (T0/T ) x , where x = 0.75 ± 0.05. Surprisingly, the exponent x was found to be constant for a wide range of R0 and T0 in all four materials, possibly implying a consistent underlying conduction mechanism. The results are discussed in terms of several different models of hopping conduction.

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Section: Introductionsupporting

confidence: 55%

Anomalous hopping exponents of ultrathin metal films

et al. 2000

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“…We show that in strongly disordered systems with time-reversal symmetry broken by external or intrinsic exchange magnetic field the cooling power can be greatly enhanced. The enhancement factor as large as 10 2 at magnetic field B ∼ 10 Tesla in 2D InSb films is predicted. A similar enhancement is found for the ultrasound attenuation.…”

mentioning

confidence: 82%

“…In this case W/n e was larger by a factor of 5 × 10 4 than the theoretical prediction for a dirty metal approaching the Anderson transition. Clearly, neither of the above cases with anomalously large cooling rate correspond to the piezoelectric type of electron-phonon coupling where the PIC does not hold and the theory predicts T 4 temperature behavior of cooling rate [9,10]. It is also dubious that the model of impurities which are only partially involved in the lattice motion [2] that also leads to enhanced cooling rate with T 4 temperature behavior, is realistic for the cases in question.…”

mentioning

confidence: 99%

Magnetic Field-Induced Giant Enhancement of Electron-Phonon Energy Transfer in Strongly Disordered Conductors

2013

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Relaxation of soft modes (e.g. charge density in gated semiconductor heterostructures, spin density in the presence of magnetic field) slowed down by disorder may lead to giant enhancement of energy transfer (cooling power) between overheated electrons and phonons at low bath temperature. We show that in strongly disordered systems with time-reversal symmetry broken by external or intrinsic exchange magnetic field the cooling power can be greatly enhanced. The enhancement factor as large as 10 2 at magnetic field B ∼ 10 Tesla in 2D InSb films is predicted. A similar enhancement is found for the ultrasound attenuation.Introduction-A number of recent experiments show that energy transfer (the cooling power) J (T e , T ph ) = J(T el ) − J(T ph ) between overheated electrons with temperature T el > T ph and phonons at low bath temperature T ph may vary by several orders of magnitude when measured per one electron per volume. The out-flux J(T ) = W T p may have different power-law temperature dependence with the exponent p both smaller and larger than the classical result p = 5 valid for pure metals. In disordered metals with complete screening of Coulomb interaction and impurities that are fully involved in the lattice motion one expects [1-3] a power law with p = 6 which corresponds to weaker energy transfer compared to the clean case. This is related with the "Pippard ineffectiveness condition" (denoted as PIC below) [4, 5] formulated for the rate of inelastic electron-phonon scattering. A very accurate experiments in metal films of Hf and Ti [6] confirmed this theoretical expectation, including the value of the pre-factor W in front of T 6 . At the same time, experiments on heavily doped Si [7] which also demonstrated the T 6 behavior, gave at low temperatures the value W/n e (n e is the carrier density) larger by a factor of 10 3 than the theoretical prediction in Ref. [1][2][3]. Surprisingly, the T 6 behavior of the cooling rate with approximately the same values of W/n e as in Ref. [7] were extracted from the recent experiments [8] on amorphous InO films showing weakly insulating behavior in magnetic field of 11T. In this case W/n e was larger by a factor of 5 × 10 4 than the theoretical prediction for a dirty metal approaching the Anderson transition. Clearly, neither of the above cases with anomalously large cooling rate correspond to the piezoelectric type of electron-phonon coupling where the PIC does not hold and the theory predicts T 4 temperature behavior of cooling rate [9,10]. It is also dubious that the model of impurities which are only partially involved in the lattice motion [2] that also leads to enhanced cooling rate with T 4 temperature behavior, is realistic for the cases in question. Thus there was a quest from experiment for a different and more general mechanism of enhancement of cooling rate in strongly disordered conductors.

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“…(5), T c vanishes at the critical conductance g cF = ln 2 ( /T c0 τ * )/(8π), (which needs to be large enough for the theory to be self-consistent). At lower (but still large compared to unity) conductances, the material never becomes superconducting; it stays metallic at least down to very low temperatures T loc ∼ ( /τ * ) exp(−4πg) where weak localization crosses over into the strong localization [29].…”

Section: Coulomb Suppression Of T C In Uniformly Disordered Thin Filmsmentioning

confidence: 99%

Fractal superconductivity near localization threshold

Фейгельман¹,

Ioffe²,

Kravtsov³

et al. 2010

Annals of Physics

238

360

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We develop a semi-quantitative theory of electron pairing and resulting superconductivity in bulk "poor conductors" in which Fermi energy E F is located in the region of localized states not so far from the Anderson mobility edge E c . We assume attractive interaction between electrons near the Fermi surface. We review the existing theories and experimental data and argue that a large class of disordered films is described by this model.Our theoretical analysis is based on analytical treatment of pairing correlations, described in the basis of the exact single-particle eigenstates of the 3D Anderson model, which we combine with numerical data on eigenfunction correlations. Fractal nature of critical wavefunction's correlations is shown to be crucial for the physics of these systems.We identify three distinct phases: 'critical' superconductive state formed at E F = E c , superconducting state with a strong pseudogap, realized due to pairing of weakly localized electrons and insulating state realized at E F still deeper inside localized band. The 'critical' superconducting phase is characterized by the enhancement of the transition temperature with respect to BCS result, by the inhomogeneous spatial distribution of superconductive order parameter and local density of states. The major new feature of the pseudo-gaped state is the presence of two independent energy scales: superconducting gap ∆, that is due to many-body correlations and a new "pseudogap" energy scale ∆ P which characterizes typical binding energy of localized electron pairs and leads to the insulating behavior of the resistivity as a function of temperature above superconductive T c . Two gap nature of the pseudogapped superconductor is shown to lead to specific features seen in scanning tunneling spectroscopy and point-contact Andreev spectroscopy. We predict that pseudogaped superconducting state demonstrates anomalous behavior of the optical spectral weight. The insulating state is realized due to presence of local pairing gap but without superconducting correlations; it is characterized by a hard insulating gap in the density of single electrons and by purely activated low-temperature resistivity ln R(T ) ∼ 1/T .Based on these results we propose a new "pseudospin" scenario of superconductorinsulator transition and argue that it is realized in a particular class of disordered superconducting films. We conclude by the discussion of the experimental predictions of the theory and the theoretical issues that remain unsolved.

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Hot-Electron Effects in Two-Dimensional Hopping with a Large Localization Length

Cited by 39 publications

References 27 publications

Anomalous hopping exponents of ultrathin metal films

Anomalous hopping exponents of ultrathin metal films

Magnetic Field-Induced Giant Enhancement of Electron-Phonon Energy Transfer in Strongly Disordered Conductors

Fractal superconductivity near localization threshold

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