Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
  • Open Access

Supercurrent distribution in real-space and anomalous paramagnetic response in a superconducting quasicrystal

Takumi Fukushima, Nayuta Takemori, Shiro Sakai, Masanori Ichioka, and Anuradha Jagannathan
Phys. Rev. Research 5, 043164 – Published 21 November 2023
PDFHTMLExport Citation
Abstract
Authors
Article Text
  • INTRODUCTION
  • MODEL AND METHOD
  • RESULTS
  • SUMMARY
  • ACKNOWLEDGMENTS
  • APPENDICES
    • References

    Abstract

    We theoretically study the real-space distribution of the supercurrent that flows under a uniform vector potential in a two-dimensional quasiperiodic structure. This is done by considering the attractive Hubbard model on the quasiperiodic Ammann-Beenker structure and studying the superconducting phase within the Bogoliubov-de Gennes mean-field theory. Decomposing the local supercurrent into the paramagnetic and diamagnetic components, we numerically investigate their dependencies on average electron density, temperature, and the angle of the applied vector potential. We find that the diamagnetic current locally violates the current conservation law, necessitating compensation from the paramagnetic current, even at zero temperature. The paramagnetic current shows exotic behaviors in the quasiperiodic structure, such as local currents, which are oriented transversally or reversely to that of the applied vector potential.

    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    • Figure
    4 More
    • Received 31 May 2023
    • Revised 29 September 2023
    • Accepted 5 November 2023

    DOI:https://doi.org/10.1103/PhysRevResearch.5.043164

    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.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Superconductors
    1. Physical Systems
    QuasicrystalsTwo-dimensional electron system
    1. Techniques
    Hubbard modelMean field theorySuperconductivity
    Condensed Matter, Materials & Applied Physics

    Authors & Affiliations

    Takumi Fukushima1,2,*, Nayuta Takemori3,4,†, Shiro Sakai4, Masanori Ichioka2, and Anuradha Jagannathan5

    • 1Institute for Solid State Physics, The University of Tokyo, Kashiwa 277-8581, Japan
    • 2Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-8530, Japan
    • 3Center for Quantum Information and Quantum Biology, Osaka University, Toyonaka 560-0043, Japan
    • 4Center for Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
    • 5Laboratoire de Physique des Solides, Université Paris-Saclay 91405 Orsay, France

    • *tfukushima@issp.u-tokyo.ac.jp
    • †nayuta.takemori.qiqb@osaka-u.ac.jp

    Article Text

    Click to Expand

    References

    Click to Expand
    Issue

    Vol. 5, Iss. 4 — November - December 2023

    Subject Areas
    Reuse & Permissions
    Author publication services for translation and copyediting assistance advertisement

    Authorization Required

    Log In
    Other Options
    ×

    Images

    • Figure 1
      Figure 1

      A part of the Ammann-Beenker structure. The structure has six different vertex patterns, with A through F assigned in descending order of coordination number Zi=8,7,...,3 [42, 43].

      Reuse & Permissions
    • Figure 2
      Figure 2

      Real-space distribution (left panels) and the coordination number Zi dependence (right panels) of the local electron density ni [(a) and (c)] and the superconducting order parameter amplitude |Δi| [(b) and (d)] on the Ammann-Beenker structure for n¯=0.3 [(a) and (b)] and 0.7 [(c) and (d)] for U=−3, T=0.01, and θ=0. For the spatial distribution, we show a part of the system consisting of about 100 sites for visibility.

      Reuse & Permissions
    • Figure 3
      Figure 3

      Real-space distribution of the local current Jj→i (left), diamagnetic current Jj→idia (middle) and paramagnetic current Jj→ipara (right) on the Ammann-Beenker structure at U=−3, T=0.01, and θ=0. The results were obtained for n¯=0.3 (a) and 0.7 (b). Length and orientation of arrows represent the strength and direction of the supercurrent on each bond. Black dots show position of the vertex. In each panel, we show a part of the system consisting of about 100 sites for visibility.

      Reuse & Permissions
    • Figure 4
      Figure 4

      Divergence (Jidia)out−(Jidia)in of the diamagnetic current on the site i at T=0.01 for (i) n¯=0.3,θ=0, (ii) n¯=0.3,θ=π8, (iii) n¯=0.7,θ=0, and (iv) n¯=0.7,θ=π8. The distributions are classified according to the coordination number Zi. The results for each Zi is plotted with the abscissa value shifted for each condition.

      Reuse & Permissions
    • Figure 5
      Figure 5

      Filling dependence of the local current Jj→i (a), diamagnetic current Jj→idia (b) and paramagnetic current Jj→ipara (c) for U=−3, T=0.01, and θ=0. The results in (a) are separated into the diamagnetic and paramagnetic components, respectively, in (b) and (c). We note that Jj→ipara flows in the opposite direction of Jj→idia. The data points for each |ϕn| are slightly shifted in the horizontal direction for the sake of visibility.

      Reuse & Permissions
    • Figure 6
      Figure 6

      Values of Jj→idia divided by the bond factor cosϕn are plotted versus njni (left column) and |ΔjΔi*| (right column) for four different fillings n¯. Parameters: U=−3,T=0.01, and θ=0.

      Reuse & Permissions
    • Figure 7
      Figure 7

      Temperature dependence of the local current Jj→i (a), diamagnetic current Jj→idia (b) and paramagnetic current Jj→ipara (c) for U=−3, n¯=0.5, and θ=0. Results on a square lattice (SL) of 900 sites are shown by black curves. The vertical dotted line represents Tc of the Ammann-Beenker structure. The results in (a) are separated into the diamagnetic and paramagnetic components, respectively, in (b) and (c). We note that Jj→ipara flows in the opposite direction of Jj→idia. The data points for each |ϕn| are slightly shifted in the horizontal direction for the sake of visibility.

      Reuse & Permissions
    • Figure 8
      Figure 8

      The same as Fig. 3, but for θ=π8.

      Reuse & Permissions
    • Figure 9
      Figure 9

      Distributions of the local current Jj→i (left panels), diamagnetic current Jj→idia (middle panels), and paramagnetic current Jj→ipara (right panels) for every π36 [rad] from θ=0 [rad] to π8 [rad] at U=−3 and T=0.01. The distribution of Jj→i at each θ is classified by the flow directions ϕn=0, π4, and −π2 for (a) n¯=0.3 and (b) n¯=0.7. The results of left pannel in (a) and (b) are separated into the diamagnetic and paramagnetic components, respectively, in the middle and the right panels. The data points for each ϕn are slightly shifted in the horizontal direction for the sake of visibility.

      Reuse & Permissions
    • Figure 10
      Figure 10

      Real-space distribution of the local supercurrent Jj→i for n¯=0.7 and θ=π36. The backflows are shown as the red downward arrows. We show a part of the system consisting of about 100 sites for visibility.

      Reuse & Permissions
    • Figure 11
      Figure 11

      Real-space distribution of the local supercurrent Jj→i on (a) the honeycomb lattice and the Penrose structure (b) and (c) at U=−3, T=0.01, n¯=0.3. (a) and (b) are for the case of θ=0 while (c) is in the case of θ=π/10. The red arrows in (c) show the vertical supercurrents against the applied vector potential. In each panel, we show a part of the system consisting of about 100 sites for visibility.

      Reuse & Permissions
    ×

    Sign up to receive regular email alerts from Physical Review Research

    Reuse & Permissions

    It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

    ×

    Log In

    Cancel
    ×

    Search

    Article Lookup

    Paste a citation or DOI
    Enter a citation
    ×