Order Parameter in Electron Systems: Its Fluctuations and Oscillations

We have studied the low-temperature electrical transport properties of Pbx(SiO2)1−x (x being the Pb volume fraction) nanogranular films with thicknesses of ∼1000 nm and x spanning the dielectric, transitional, and metallic regions. It is found that the percolation threshold xc lies between 0.57 and 0.60. For films with x 0.50, the resistivities ρ as functions of temperature T obey ρ ∝ exp(∆/kBT ) relation (∆ being the local superconducting gap and the kB Boltzmann constant) below the superconducting transition temperature Tc (∼7 K) of Pb granules. The value of the gap obtained via this expression is almost identical to that by single electron tunneling spectra measurement. The magnetoresistance is negative below Tc and its absolute value is far larger than that above Tc at a certain field. These observations indicate that single electron hopping (or tunneling), rather than Cooper pair hopping (or tunneling) governs the transport processes below Tc. The temperature dependence of resistivities shows reentrant behavior for the 0.50

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“…(2) could be naturally obtained [54]. Firstly, we assume ∆ to be a constant and designate it by ∆ 01 .…”

Section: Resultsmentioning

confidence: 99%

Hopping conductance and macroscopic quantum tunneling effect in three dimensional Pbx(SiO2)1−x nanogranular films

Duan

Yang

et al. 2019

Phys. Rev. B

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“…In full analogy with the above discussion of the supervector theory for n = 1, one can perform the structural averaging over the RRG ensemble, which reduces the theory (6) to an integral over functions F (Q). The corresponding self-consistency equation has the form (30) and is identical to the self-consistency equation for the σ model on an infinite Bethe lattice [42][43][44][45][46][47]. In the localized phase (and at the critical point), the solution (in the limit η → 0) is g 0 (Q) = 1, which corresponds to preserved symmetry.…”

Section: B Field-theoretical Approachmentioning

confidence: 92%

Statistics of eigenstates near the localization transition on random regular graphs

2019

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Dynamical and spatial correlations of eigenfunctions as well as energy level correlations in the Anderson model on random regular graphs (RRG) are studied. We consider the critical point of the Anderson transition and the delocalized phase. In the delocalized phase near the transition point, the observables show a broad critical regime for system sizes N below the correlation volume N ξ and then cross over to the ergodic behavior. Eigenstate correlations allow us to visualize the correlation length ξ ∼ log N ξ that controls the finite-size scaling near the transition. The critical-to-ergodic crossover is very peculiar, since the critical point is similar to the localized phase, whereas the ergodic regime is characterized by very fast "diffusion" which is similar to the ballistic transport. In particular, the return probability crosses over from a logarithmically slow variation with time in the critical regime to an exponentially fast decay in the ergodic regime. Spectral correlations in the delocalized phase near the transition are characterized by level number variance Σ2(ω) crossing over, with increasing freqyency ω, from ergodic behavior Σ2 = 2/π 2 ln ω/∆ to Σ2 ∝ ω 2 at ωc ∼ (N N ξ ) −1/2 and finally to Poissonian behavior Σ2 = ω/∆ at ω ξ ∼ N −1 ξ . We find a perfect agreement between results of exact diagonalization and those resulting from the solution of the self-consistency equation obtained within the saddle-point analysis of the effective supersymmetric action. We show that the RRG model can be viewed as an intricate d → ∞ limit of the Anderson model in d spatial dimensions.arXiv:1810.11444v1 [cond-mat.dis-nn]

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“…In the large-N limit, the integral can be evaluated by the saddle-point method. The corresponding saddle-point equation has a form analogous to the self-consistency equations obtained for the Anderson model [13,14] and the σ model [15][16][17][18][19][20] on an infinite Bethe lattice.…”

Section: Introductionmentioning

confidence: 87%

Critical behavior at the localization transition on random regular graphs

2019

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We study numerically the critical behavior at the localization transition in the Anderson model on infinite Bethe lattice and on random regular graphs. The focus is on the case of coordination number m+1 = 3, with a box distribution of disorder and in the middle of the band (energy E = 0), which is the model most frequently considered in the literature. As a first step, we carry out an accurate determination of the critical disorder, with the result Wc = 18.17 ± 0.01. After this, we determine the dependence of the correlation volume N ξ = m ξ (where ξ is the associated correlation length) on disorder W on the delocalized side of the transition, W < Wc, by means of population dynamics. The asymptotic critical behavior is found to be ξ ∝ (Wc − W ) −1/2 , in agreement with analytical prediction. We find very pronounced corrections to scaling, in similarity with models in high spatial dimensionality and with many-body localization transitions. arXiv:1903.07877v2 [cond-mat.dis-nn]

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Order Parameter in Electron Systems: Its Fluctuations and Oscillations

Cited by 24 publications

References 69 publications

Hopping conductance and macroscopic quantum tunneling effect in three dimensional Pbx(SiO2)1−x nanogranular films

Hopping conductance and macroscopic quantum tunneling effect in three dimensional Pbx(SiO2)1−x nanogranular films

Statistics of eigenstates near the localization transition on random regular graphs

Critical behavior at the localization transition on random regular graphs

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