Nucleation and growth of the superconducting phase in the presence of a current

Andrew J. Dolgert, Thomas Blum, Alan T. Dorsey, and Michael Fowler
Phys. Rev. B 57, 5432 – Published 1 March 1998
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Abstract

We study the localized stationary solutions of the one-dimensional time-dependent Ginzburg-Landau equations in the presence of a current. These threshold perturbations separate undercritical perturbations which return to the normal phase from overcritical perturbations which lead to the superconducting phase. Careful numerical work in the small-current limit shows that the amplitude of these solutions is exponentially small in the current; we provide an approximate analysis which captures this behavior. As the current is increased toward the stall current J*, the width of these solutions diverges, resulting in widely separated normal-superconducting interfaces. We map out numerically the dependence of J* on u (a parameter characterizing the material) and use asymptotic analysis to derive the behaviors for large u (J*u1/4) and small u (JJc, the critical depairing current), which agree with the numerical work in these regimes. For currents other than J* the interface moves, and in this case we study the interface velocity as a function of u and J. We find that the velocities are bounded both as J0 and as JJc, contrary to previous claims.

  • Received 9 September 1997

DOI:https://doi.org/10.1103/PhysRevB.57.5432

©1998 American Physical Society

Authors & Affiliations

Andrew J. Dolgert* and Thomas Blum

  • Department of Physics, University of Virginia, McCormick Road, Charlottesville, Virginia 22901

Alan T. Dorsey

  • Department of Physics, University of Florida, Gainesville, Florida 32611

Michael Fowler§

  • Department of Physics, University of Virginia, McCormick Road, Charlottesville, Virginia 22901

  • *Electronic address: ajd2m@virginia.edu
  • Electronic address: teb2n@virginia.edu
  • Electronic address: dorsey@phys.ufl.edu
  • §Electronic address: mf1i@virginia.edu

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Vol. 57, Iss. 9 — 1 March 1998

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