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Effective dimensionality crossover for superconducting surfaces in parallel magnetic fields

Effective dimensionality crossover for superconducting surfaces in parallel magnetic fields The superconducting fluctuations above T c in the presence of a magnetic field parallel to the surface are known to be one dimensional (1D) in the bulk and 2D near the surface. The crossover between these two behaviors is studied as a function of the surface boundary condition on the order parameter. Similar effects can be obtained due to the proximity of an additional surface, in the case of a film, as found by Thompson. The parameter governing the crossover is an effective mass related to the dependence of the eigenvalue of the Ginzburg-Landau equation on the distance from the surface. Predictions for the surface specific heat and static impedance and their crossovers from 1D to 2D behaviors are obtained. For a film with a "critical" thickness of ∼ 1.8 ξ T , Gaussian exponents of 5/4 for the divergences of the above quantities are obtained. This corresponds to an effective dimensionality of 3/2, and is due to the fact that the dependence of the Ginzburg-Landau free energy on one of the momentum components becomes quartic. The same happens more generally in other k -space instabilities (Lifschitz multicritical points). The statement about the above effective change in dimensionality is also proved to order ε = 4 - d in a renormalization-group calculation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Physical Review B American Physical Society (APS)

Effective dimensionality crossover for superconducting surfaces in parallel magnetic fields

Imry, Y
Physical Review B , Volume 15 (1) – Jan 1, 1977
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Publisher
American Physical Society (APS)
Copyright
Copyright © 1977 The American Physical Society
ISSN
1095-3795
DOI
10.1103/PhysRevB.15.230
Publisher site
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Abstract

The superconducting fluctuations above T c in the presence of a magnetic field parallel to the surface are known to be one dimensional (1D) in the bulk and 2D near the surface. The crossover between these two behaviors is studied as a function of the surface boundary condition on the order parameter. Similar effects can be obtained due to the proximity of an additional surface, in the case of a film, as found by Thompson. The parameter governing the crossover is an effective mass related to the dependence of the eigenvalue of the Ginzburg-Landau equation on the distance from the surface. Predictions for the surface specific heat and static impedance and their crossovers from 1D to 2D behaviors are obtained. For a film with a "critical" thickness of ∼ 1.8 ξ T , Gaussian exponents of 5/4 for the divergences of the above quantities are obtained. This corresponds to an effective dimensionality of 3/2, and is due to the fact that the dependence of the Ginzburg-Landau free energy on one of the momentum components becomes quartic. The same happens more generally in other k -space instabilities (Lifschitz multicritical points). The statement about the above effective change in dimensionality is also proved to order ε = 4 - d in a renormalization-group calculation.

Journal

Physical Review B – American Physical Society (APS)

Published: Jan 1, 1977

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