Fractal superconductivity near localization threshold

Фейгельман, М. В.; Ioffe, L. B.; Kravtsov, V. E.; Cuevas, E.

doi:10.1016/j.aop.2010.04.001

Cited by 238 publications

(383 citation statements)

References 119 publications

(403 reference statements)

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“…Following this relationship, the experiments on the B-SIT and the experiments tuning the carrier density form a dual set of experiments. Interestingly, this analogy implies that the disorder-driven SIT at B = 0 must have a different mechanism for the insulating state; a distinction that cannot be made from experiments: Transport and scanning tunnelling experiments [24][25][26] as well as microscopic model calculations 27,28 suggest that Cooper pairs persist also in the disorder-driven insulating state.…”

Section: T0/2tmentioning

confidence: 99%

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

et al. 2013

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The superconductor-insulator transition (SIT) is an accessible quantum phase transition 1,2 that is observed in a number of systems and can be driven by various experimental means 3-9 . A central outstanding issue regards the physical nature of the insulating phase terminating superconductivity 10 . Theoretical advances led to the proposition that this insulator is a new state of matter, termed a superinsulator 11,12 , because its properties can be inferred from the superconductor by invoking duality symmetry 13 . Here we report on the observation of duality symmetry near the magnetic-field-driven SIT in amorphous indium oxide. However, we show that the symmetry is broken by the emergence of the strong insulating state at low temperature.For the magnetic-field-driven SIT (B-SIT) in disordered films, the concept of vortex-charge duality was investigated in ref. 14, using the dirty boson model. In the superconductor, Cooper pairs are condensed into a superfluid at low temperature (T ) values leading to a zero resistivity (ρ) state, with vortices as bosonic excitations introducing dissipation and causing finite ρ. According to the duality concept, in the insulating state, vortices are condensed in a collective mode with zero conductivity (σ ), and the Cooper pairs are the bosonic excitation contributing to a finite σ .The vortex-charge duality has also been applied to the analysis of Josephson junction arrays 15,16 , which are often used as a model system for the SIT in disordered films 11,12,17 . In these systems the insulating state is commonly ascribed to a Coulomb blockade of superconducting islands. Duality is also applied to many other systems, for example, boson duality in two-dimensional electron gases 18 . Recently, evidence for the vortex-charge duality near a SIT was found in LaAlO 3 /SrTiO 3 interfaces 13 .Here, we experimentally investigate the duality symmetry across the B-SIT. We apply a duality transformation relating states within the superconductor to states in the B-driven insulator. We observe vortex-charge duality symmetry that holds up to one order of magnitude in B, T and ρ. The new aspect of this work is that we find systematic deviations from duality symmetry that originate in the B-induced magnetoresistance (ρ(B)) peak 5 . These deviations are qualitatively different at low and high T , as will be shown in detail below.In Fig. 1 we present ρ(B) isotherms obtained from sample RAM005b, which is superconducting at B = 0 with T c = 1.3 K. For all T values where reliable Ohmic data could be collected ρ increases with B until it reaches a T -dependent peak at B peak between 8.5-9.7 T. We restrict ourselves to T > 0.15 K because in the insulating phase, at T < 0.15 K, severe bi-stability of the electron T develops 19 , resulting in strongly nonlinear I -V , that prevented reliable measurements of ρ.The isotherms exhibit a weakly T -dependent crossing point close to h/(2e) 2 , where h is Planck's constant and 2e is the charge

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Section: T0/2tmentioning

confidence: 99%

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

et al. 2013

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“…Multifractality can moreover influence the behavior of various systems near criticality in different ways. For example, the large overlap of multifractal wave-functions can increase the superconducting critical temperature 8 . The multifractality of the local density of states may induce a new phase because of the presence of local Kondo effects induced by local pseudogaps at the Fermi energy 9 .…”

Section: Introductionmentioning

confidence: 99%

Anderson transition and multifractals in the spectrum of the Dirac operator of quantum chromodynamics at high temperature

et al. 2015

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We investigate the Anderson transition found in the spectrum of the Dirac operator of Quantum Chromodynamics (QCD) at high temperature, studying the properties of the critical quark eigenfunctions. Applying multifractal finite-size scaling we determine the critical point and the critical exponent of the transition, finding agreement with previous results, and with available results for the unitary Anderson model. We estimate several multifractal exponents, finding also in this case agreement with a recent determination for the unitary Anderson model. Our results confirm the presence of a true Anderson localization-delocalization transition in the spectrum of the quark Dirac operator at high-temperature, and further support that it belongs to the 3D unitary Anderson model class.

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“…These phenomena led to a lot of interesting theoretical work [11][12][13][14][15][16][17][18] , which were to a great extent spurred by an experimental feature of many strongly disordered films with superconducting correlations -a giant magnetoresistance peak -for which a full theoretical understanding is still lacking. Nevertheless, it was already understood in Ref.…”

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confidence: 99%

Two-component Coulomb glass in insulators with a local attraction

et al. 2012

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Motivated by evidence of local electron-electron attraction in experiments on disordered insulating films, we propose a new two-component Coulomb glass model that combines strong disorder and long-range Coulomb repulsion with the additional possibility of local pockets of a short-range interelectron attraction. This model hosts a variety of interesting phenomena, in particular a crucial modification of the Coulomb gap previously believed to be universal. Tuning the short-range interaction to be repulsive, we find non-monotonic humps in the density of states within the Coulomb gap. We further study variable-range hopping transport in such systems by extending the standard resistor network approach to include the motion of both single electrons and local pairs. In certain parameter regimes the competition between these two types of carriers results in a distinct peak in resistance as a function of the local attraction strength, which can be tuned by a magnetic field.

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Fractal superconductivity near localization threshold

Cited by 238 publications

References 119 publications

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

Duality symmetry and its breakdown in the vicinity of the superconductor–insulator transition

Anderson transition and multifractals in the spectrum of the Dirac operator of quantum chromodynamics at high temperature

Two-component Coulomb glass in insulators with a local attraction

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