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Superconductivity on a quasiperiodic lattice: Extended-to-localized crossover of Cooper pairs

Shiro Sakai, Nayuta Takemori, Akihisa Koga, and Ryotaro Arita
Phys. Rev. B 95, 024509 – Published 18 January 2017
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    Abstract

    We study a possible superconductivity in quasiperiodic systems by portraying the issue within the attractive Hubbard model on a Penrose lattice. Applying a real-space dynamical mean-field theory to the model consisting of 4181 sites, we find a superconducting phase at low temperatures. Reflecting the nonperiodicity of the Penrose lattice, the superconducting state exhibits an inhomogeneity. According to the type of the inhomogeneity, the superconducting phase is categorized into three different regions which cross over each other. Among them, the weak-coupling region exhibits spatially extended Cooper pairs, which are nevertheless distinct from the conventional pairing of two electrons with opposite momenta.

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    • Received 12 August 2016
    • Revised 20 November 2016

    DOI:https://doi.org/10.1103/PhysRevB.95.024509

    ©2017 American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Fermionic condensatesSuperconductivity
    1. Physical Systems
    QuasicrystalsUnconventional superconductors
    1. Techniques
    Dynamical mean field theoryHubbard model
    Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

    Authors & Affiliations

    Shiro Sakai1, Nayuta Takemori1, Akihisa Koga2, and Ryotaro Arita1

    • 1Center For Emergent Matter Science, RIKEN, Wako, Saitama 351-0198, Japan
    • 2Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551, Japan

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    Issue

    Vol. 95, Iss. 2 — 1 January 2017

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    Images

    • Figure 1
      Figure 1

      Two-dimensional Penrose lattice of 4181 sites. The sites are located at vertices of rhombuses. Top-right panel is an enlarged view of a part of the lattice.

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    • Figure 2
      Figure 2

      (a) T dependence of OPi (red crosses) and OP¯ (black dots) for n¯=0.5 and U=−4. Blue curve plots the DMFT results for the Bethe lattice with the bandwidth 8t at quarter filling. (b) The same for U dependence for n¯=0.5 and T=0.01.

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    • Figure 3
      Figure 3

      Spatial patterns of OPi and ni at T=0.01 for three different sets of U and n¯. The sites with Qi>Q¯(Qi<Q¯) with Q=OP and n are colored by red (yellow).

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    • Figure 4
      Figure 4

      OPi plotted against ni/2(1−ni/2) for various sets of n¯ and U at T=0.01. In order of (a)-(b)-(f)-(c)-(d), |U| increases at a fixed n¯=0.5. In order of (e)-(f)-(g)-(h), n¯ increases at a fixed U=−8. Thick gray dashed curve in (d) shows the result calculated for the infinite-dimensional Bethe lattice with the bandwidth 8t.

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    • Figure 5
      Figure 5

      (a) Off-site pair amplitude OPij≡〈ci↑cj↓〉 (normalized by OP¯) plotted against the Euclidean distance ||ri−rj|| for the three states shown in Fig. 3. Inset: Enlarged view for the short-distance part of red triangles and blue crosses. (b) and (c) Intensity map of |OPkk′| calculated for a square lattice with the bandwidth 8t at quarter filling for U=−2 and −16, respectively. Just for plotting purpose, we set kx=ky=k and kx′=ky′=k′. (d)–(f) The same quantity for the three states in (a), plotted with a cutoff at |k|,|k′|=10.

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    • Figure 6
      Figure 6

      Phase diagram on the n¯−U plane at T=0.01. SC denotes the superconducting phase. The yellow, red, and blue regions, which are judged from the characteristics seen in the OPi−ni/2(1−ni/2) plots like Fig. 4, denote the superconducting states represented by Figs. 3, 3, and 3, respectively.

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