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Renormalization of Competing Interactions and Superconductivity on Small Scales

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Abstract

The interaction-induced orbital magnetic response of a nanoscale ring is evaluated for a diffusive system which is a superconductor in the bulk. The interplay of the renormalized Coulomb and Fröhlich interactions is crucial. The magnetic susceptibility which results from the fluctuations of the uniform superconducting order parameter is diamagnetic (paramagnetic) when the renormalized combined interaction is attractive (repulsive). Above the transition temperature of the bulk the total magnetic susceptibility has contributions from many wave-vector- and (Matsubara) frequency-dependent order parameter fluctuations. Each of these contributions results from a different renormalization of the relevant coupling energy, when one integrates out the fermionic degrees of freedom. The total diamagnetic response of the large superconductor may become paramagnetic when the system’s size decreases.

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Notes

  1. Here, high temperatures are above the Ginzburg region, in which one must include higher order terms. The Ginzburg criterion was discussed by Aharony et al. [21].

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Acknowledgments

We thank Yuval Oreg and Alexander Finkelstein for important discussions, and Hamutal Bary-Soroker for participation in Ref. [10], which led to the present work. This work was supported by the Israeli Science Foundation (ISF) and the US-Israel Binational Science Foundation (BSF).

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Authors and Affiliations

  1. Department of Physics, Ben Gurion University, 84105, Beer Sheva, Israel

    A. Aharony & O. Entin-Wohlman

  2. Raymond and Beverly Sackler School of Physics and Astronomy, Tel Aviv University, 69978, Tel Aviv, Israel

    A. Aharony & O. Entin-Wohlman

  3. Department of Condensed Matter Physics, Weizmann Institute of Science, 76100, Rehovot, Israel

    Y. Imry

Authors
  1. A. Aharony
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  2. O. Entin-Wohlman
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  3. Y. Imry
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Correspondence to A. Aharony.

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Aharony, A., Entin-Wohlman, O. & Imry, Y. Renormalization of Competing Interactions and Superconductivity on Small Scales. J Stat Phys 157, 979–989 (2014). https://doi.org/10.1007/s10955-014-1100-1

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  • DOI: https://doi.org/10.1007/s10955-014-1100-1

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