Fluctuation conductivity of inhomogeneous superconductors: A fractal aggregation model

Gusmo, M. A.; Mors, Paulo Machado

doi:10.1103/physrevb.42.10030

Cited by 13 publications

(3 citation statements)

References 16 publications

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“…18 The fractal model of Gusmao and Mors helps to explain the nonintegral dimensionality observed in paraconductivity analysis in some HTS materials. 19 Equations ͑4͒ give the values of A for 2D and 3D thermodynamic fluctuations for the Aslamazov and Larkin model, larger values of are indicative of even lower dimensionality, ϭ1.5 for 1D and ϭ2 for 0D.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Paraconductivity in YBa2Cu3O7 and YBa2Cu3O7 thin film composites with cerium oxide and gold

Cukauskas¹,

Allen²

1998

Journal of Applied Physics

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The paraconductivity for thin films of YBa2Cu3O7 (YBCO) and composites of YBCO with CeO2 and gold was investigated and analyzed using the Aslamazov and Larkin theory. Plain YBCO thin films sputter deposited on MgO, SrTiO3, and yttrium stabilized zirconium typically showed no dimensional crossover, were described by three dimensional (3D) fluctuation conductivity, and had a critical slope just above the critical region in agreement with the prediction of theory. With few exceptions, the CeO2 and gold composite films showed a dimensional crossover and a reduced critical exponent. The change in dimensionality was typically from 3D to two dimensional (2D) fluctuation conductivity. These composite films all had reduced values for the critical exponent which we attribute to an enlarged or extended critical region. This is in agreement with the critical current response of these composites to small magnetic fields. Additionally, the composites showed a two step transition in the paraconductivity and a minimum below the critical region. The subsequent fall-off to the zero resistance state was characterized by two different slopes. Lastly, the paraconductivity was related to film degradation resulting from photoresist processing and time storage. Dimensionality changes were observed due to this degradation.

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Section: Theoretical Backgroundmentioning

confidence: 99%

Paraconductivity in YBa2Cu3O7 and YBa2Cu3O7 thin film composites with cerium oxide and gold

Cukauskas¹,

Allen²

1998

Journal of Applied Physics

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“…where ̅ is the respective fractal dimension of the superconducting aggregate. The fractal character of the superconducting fluctuations have been reported in the Y123 superconductor in previous works, 14,24,27 but not for Y358 superconductor. This fractal regime is described by the exponent λ3D↔2D = 0.74 ± 0.05.…”

Section: Gaussian Fluctuationsmentioning

confidence: 80%

Gaussian and critical scalings in the magnetoconductivity fluctuations of Y₃Ba₅Cu₈O₁₈ superconductor

Dias

Vieira

Oliveira

et al. 2018

Int. J. Mod. Phys. B

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We have studied the superconducting transition and the magnetoconductivity fluctuations in the polycrystalline Y3Ba5Cu8O[Formula: see text] (Y358) superconductor under magnetic fields upto 1 T. A two-step superconducting transition could be observed as a consequence of the granular structure of the sample, which is strongly affected by the applied magnetic field. Gaussian and genuine critical 3D-XY-E fluctuation regimes were identified. A critical scaling regime beyond 3D-XY was identified for magnetic fields upto 0.25 T, corresponding to the averaged exponent 0.19 and suggesting the occurrence of the weak first-order character of the superconducting transition. In the approximation to the zero resistance a power law regime could be observed, corresponding to the averaged exponent 2.37, which are smaller than previously reported for the Y358 system. Our results are discussed in terms of the Y358 and YBa2Cu3O[Formula: see text](Y123) results in the literature.

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“…In the field of superconductivity, fractal geometry was used in [26] to explain the irregular fluctuation conductivity detected in inhomogeneous superconducting materials. A fractal aggregation model to simulate fluctuation conductivity of inhomogeneous superconductors was done in [27]. The analysis of inhomogeneous superconductors is important due to the crucial role of inhomogeneities in polycrystalline high critical temperature superconductors [28].…”

Section: Introductionmentioning

confidence: 99%

Superconductivity and nucleation from fractal anisotropy and product-like fractal measure

El-Nabulsi

2021

Proc. R. Soc. A.

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Superconductivity is analysed based on the product-like fractal measure approach with fractal dimension α introduced by Li and Ostoja-Starzewski in their attempt to explore anisotropic fractal elastic media. Our study shows the emergence of a massless state at the boundary of the superconductor and the simultaneous occurrence of isothermal and adiabatic processes in the superconductor depending on the position of the electrons. Several physical quantities were found to be position-dependent comparable with those arising in heavy doping and p–n junction. At the boundary of the superconductor, a shrinkage of the magnetic field was observed, leading to a scenario equivalent to the Meissner–Ochsenfeld effect. An enhancement of the London penetration depth is revealed and such an improvement was observed in pnictides at the onset of commensurate spin-density-wave order inside the superconducting phase at zero temperature. The Bardeen–Cooper–Schrieffer theory was also analysed and the appearance of zero-energy states is detected. Nucleation of superconductivity in a bulk was also studied. The system acts as a quantum damped harmonic oscillator and our analysis showed that type-I superconductivity occurs when κ < 2 / ( 1 + α ) , whereas type II occurs for κ > 2 / ( 1 + α ) , where κ is the Ginzburg–Landau parameter. The transition at the passage from the ‘genuine’ to the ‘intermediate’ type-I estimates 0.767767 < α ≤ 1 .

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Fluctuation conductivity of inhomogeneous superconductors: A fractal aggregation model

Cited by 13 publications

References 16 publications

Paraconductivity in YBa2Cu3O7 and YBa2Cu3O7 thin film composites with cerium oxide and gold

Paraconductivity in YBa2Cu3O7 and YBa2Cu3O7 thin film composites with cerium oxide and gold

Gaussian and critical scalings in the magnetoconductivity fluctuations of Y₃Ba₅Cu₈O₁₈ superconductor

Superconductivity and nucleation from fractal anisotropy and product-like fractal measure

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Fluctuation conductivity of inhomogeneous superconductors: A fractal aggregation model

Cited by 13 publications

References 16 publications

Paraconductivity in YBa2Cu3O7 and YBa2Cu3O7 thin film composites with cerium oxide and gold

Paraconductivity in YBa2Cu3O7 and YBa2Cu3O7 thin film composites with cerium oxide and gold

Gaussian and critical scalings in the magnetoconductivity fluctuations of Y3Ba5Cu8O18 superconductor

Superconductivity and nucleation from fractal anisotropy and product-like fractal measure

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Gaussian and critical scalings in the magnetoconductivity fluctuations of Y₃Ba₅Cu₈O₁₈ superconductor