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Scaling, Finite Size Effects, and Crossovers of the Resistivity and Current-Voltage Characteristics in Two-Dimensional Superconductors
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.
KTH, School of Engineering Sciences (SCI), Theoretical Physics, Statistical Physics.ORCID iD: 0000-0002-9881-7857
(English)Manuscript (preprint) (Other academic)
Abstract [en]

We revisit the scaling properties of the resistivity and the current-voltage characteristics at and below the Berezinskii-Kosterlitz-Thouless transition, both in zero and nonzero magnetic field. The scaling properties are derived by integrating the renormalization group flow equations up to a scale where they can be reliably matched to simple analytic expressions. The vortex fugacity turns out to be dangerously irrelevant for these quantities below $T_c$, thereby altering the scaling behavior. We derive the possible crossover effects as the current, magnetic field or system size is varied, and find a strong multiplicative logarithmic correction near $T_c$, all which is necessary to account for when interpreting experiments and simulation data. Our analysis clarifies a longstanding discrepancy between the finite size dependence found in many simulations and the current-voltage characteristics of experiments. We further show that the logarithmic correction can be avoided by approaching the transition in a magnetic field, thereby simplifying the scaling analysis. We confirm our results by large scale numerical simulations, and calculate the dynamic critical exponent $z$, for relaxational Langevin dynamics and for resistively and capacitively shunted Josephson junction dynamics.

National Category
Condensed Matter Physics
URN: urn:nbn:se:kth:diva-96033OAI: diva2:529372
QS 2012Available from: 2012-05-30 Created: 2012-05-30 Last updated: 2012-05-30Bibliographically approved
In thesis
1. Phase fluctuation phenomena in superconductors
Open this publication in new window or tab >>Phase fluctuation phenomena in superconductors
2012 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2012. ix, 65 p.
Trita-FYS, ISSN 0280-316X ; 2012:28
National Category
Condensed Matter Physics
urn:nbn:se:kth:diva-95464 (URN)978-91-7501-380-0 (ISBN)
Public defence
2012-06-14, FB42, Albanova University Center, Roslagstullsbacken 21, Stockholm, 10:00 (English)
QC 20120530Available from: 2012-05-30 Created: 2012-05-25 Last updated: 2012-05-30Bibliographically approved

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