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Effect of disorder on coherent quantum phase slips in Josephson junction chains

A. E. Svetogorov and D. M. Basko
Phys. Rev. B 98, 054513 – Published 21 August 2018
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  • INTRODUCTION
  • STATEMENT OF THE PROBLEM
  • SPATIALLY INHOMOGENEOUS LOOP: CORRECTION…
  • INHOMOGENEOUS SUPERCONDUCTING WIRES
  • CONCLUSIONS AND OUTLOOK
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We study coherent quantum phase slips in a Josephson junction chain, including two types of quenched disorder: random spatial modulation of the junction areas and random induced background charges. Usually, the quantum phase-slip amplitude is sensitive to the normal-mode structure of superconducting phase oscillations in the ring (Mooij-Schön modes, which are all localized by the area disorder). However, we show that the modes' contribution to the disorder-induced phase-slip action fluctuations is small, and the fluctuations of the action on different junctions are mainly determined by the local junction parameters. We study the statistics of the total quantum phase-slip amplitude on the chain and show that it can be non-Gaussian for not sufficiently long chains.

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    • Received 25 June 2018
    • Revised 6 August 2018

    DOI:https://doi.org/10.1103/PhysRevB.98.054513

    ©2018 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Phase slipsSuperconductivity
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    A. E. Svetogorov1,2 and D. M. Basko1

    • 1Laboratoire de Physique et Modélisation des Milieux Condensés, Université de Grenoble-Alpes and CNRS, 25 rue des Martyrs, 38042 Grenoble, France
    • 2Moscow Institute of Physics and Technology, 141700 Dolgoprudny, Russia

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    Issue

    Vol. 98, Iss. 5 — 1 August 2018

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    Images

    • Figure 1
      Figure 1

      A schematic representation of a superconducting ring threaded by a magnetic flux Φ and containing N Josephson junctions with a capacitance C between the neighboring islands and a capacitance Cg to the ground. EJ is the Josephson energy. ϕn is the condensate phase of the nth superconducting island.

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    • Figure 2
      Figure 2

      A schematic representation of flux dependence for the ground-state energy (top panel) and persistent current (bottom panel). The gray dotted lines correspond to the purely classical approximation [i.e., neglecting the kinetic terms in the action (1)] for the static configurations ϕn=2πn/N,ϕn=0, and ϕn=−2πn/N (the left, middle, and right parabolas in the top panel, respectively). The red solid lines correspond to the exact ground state including the effect of the quantum tunneling.

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    • Figure 3
      Figure 3

      Distribution f(A) in the absence of induced charges, calculated for σ=4 and different N by direct numerical sampling (blue dots), using the weakest-junction approximation (21) (red dashed lines), the saddle-point approximation (19) (orange dotted lines), and the lognormal fit (solid green lines).

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    • Figure 4
      Figure 4

      Cumulative probability distribution of δSn and estimates of the two smallest δSn for a typical sample.

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    • Figure 5
      Figure 5

      Distribution f(|A|) with random induced charges, calculated for σ=4 and different N by direct numerical sampling (blue dots) and using the weakest-junction approximation (21) (red dashed lines).

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    • Figure 6
      Figure 6

      Two factors of the integrand in I(z) (B5), exp(−x22σ2) (dashed blue line) and 1−exp−ze−x (dashed green line), and their product (solid red line).

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