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  • Letter
  • Open Access

Resistance of two-dimensional superconducting films

E. J. König1, I. V. Protopopov2,3, A. Levchenko4, I. V. Gornyi5,6,7, and A. D. Mirlin5,6,3,8

  • 1Max Planck Institute for Solid State Research, D-70569 Stuttgart, Germany
  • 2Department of Theoretical Physics, University of Geneva, 1211 Geneva, Switzerland
  • 3L. D. Landau Institute for Theoretical Physics RAS, 119334 Moscow, Russia
  • 4Department of Physics, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
  • 5Institute for Quantum Materials and Technologies, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
  • 6Institut für Theorie der kondensierten Materie, Karlsruhe Institute of Technology, 76128 Karlsruhe, Germany
  • 7Ioffe Institute, 194021 St. Petersburg, Russia
  • 8Petersburg Nuclear Physics Institute, 188300 St. Petersburg, Russia

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Phys. Rev. B 104, L100507 – Published 29 September, 2021

DOI: https://doi.org/10.1103/PhysRevB.104.L100507

Abstract

We consider the problem of finite resistance R in superconducting films with geometry of a strip of width W near zero temperature. The resistance is generated by vortex configurations of the phase field. In the first type of process, quantum phase slip, the vortex world line in 2+1 dimensional space-time is spacelike (i.e., the superconducting phase winds in time and space). In the second type, vortex tunneling, the world line is timelike (i.e., the phase winds in the two spatial directions) and connects opposite edges of the film. For moderately disordered samples, processes of the second type favor a train of vortices, each of which tunnels only across a fraction of the sample. Optimization with respect to the number of vortices yields a tunneling distance of the order of the coherence length ξ, and the train of vortices becomes equivalent to a quantum phase slip. Based on this theory, we find the resistance lnR∼−gW/ξ, where g is the dimensionless normal-state conductance. Incorporation of quantum fluctuations indicates a quantum phase transition to an insulating state for g≲1.

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Information

Phys. Rev. B 104, L100507– Published 29 September, 2021
  • Received 27 June 2021
  • Revised 8 September 2021
  • Accepted 9 September 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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