Research ArticleSUPERCONDUCTIVITY

Correlation-induced superconductivity dynamically stabilized and enhanced by laser irradiation

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Science Advances  18 Aug 2017:
Vol. 3, no. 8, e1700718
DOI: 10.1126/sciadv.1700718
  • Fig. 1 Interaction dependence of physical quantities for superconducting states at zero-temperature equilibrium.

    (A) Long-range average of the superconducting correlation Embedded Image in two-dimensional Hubbard model. The open and solid symbols represent the results for size L × L = 8 × 8, δ ≈ 0.06 and 16 × 16, δ ≈ 0.1, respectively. Green triangles (upside-down triangles) and blue circles represent the results of charge-uniform and inhomogeneous ground states (GS), respectively. The red square (diamond) symbols represent the results for charge-uniform metastable excited states (ES). The shaded regions are guides for the eyes. The blue and red arrows represent equilibrium path and hypothetical nonequilibrium process toward uniform excited states with enhanced superconductivity by the laser irradiation A(t), respectively. Error bars indicate the statistical errors arising from the Monte Carlo sampling, but most of them are smaller than the symbol sizes here and in the following figures. (B) Energy difference per site between the uniform state with strong superconductivity and the inhomogeneous state with the weak superconductivity for L = 8 and δ ≈ 0.06. Insets represent the charge distribution ni of the uniform state for U/thop = 5 (left top), that of the inhomogeneous state for U/thop = 10 (right top), and the amplitude of the density inhomogeneity in the ground states (right bottom) respectively.

  • Fig. 2 Time dependence of Embedded Image induced by strong laser in the two-dimensional Hubbard model.

    Parameter set is (δ, L, U/thop, ω/thop, tc) = (0.0625, 8, 5.0, 15, 60) on an 8 × 8 lattice. Red circles and green squares represent the results for A0 = 1.0 and A0 = 0.75, respectively. Red solid and broken green lines indicate corresponding values of Embedded Image obtained from VMC for the charge-uniform superconducting states by assuming the effective enhancement of U/thop. Black dash dotted line is the equilibrium value in the absence of the laser irradiation. Insets represent the charge distributions n(r) for A0 = 1.0 at t = 130 and 210, corresponding to a peak and a bottom of the oscillation, respectively.

  • Fig. 3 Real part of optical conductivity of the superconducting state.

    The parameters are L = 8, δ = 0.06, and U/thop = 5.78. The results (red curves with symbols) are obtained by using the VMC method combined with a numerical procedure used in the study by Shao et al. (32). Error bars indicate the statistical errors arising from the Monte Carlo sampling. The inset shows a wider range of ω dependence. The blue solid line is a fitting obtained by a sum of two Lorentzian curves (dashed and dotted lines).

  • Fig. 4 Time dependence of double occupation in short time scale around t = 100 for the same case as Fig. 2 for A0 = 1.0.

    The black curve shows time evolution of electric field Embedded Image. The dotted line represents the zero line of the electric field.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/8/e1700718/DC1

    Supplementary Text (sections SA to SC)

    fig. S1. Superconducting correlation functions at furthest site Pd(|r| = rmax) in equilibrium and nonequilibrium obtained from the exact calculations.

    fig. S2. Dynamics of the superconducting correlations in two-dimensional Hubbard model for L = 4 and δ = 0.25 calculated from the exact Schrӧdinger dynamics.

    fig. S3. Time dependence of E/Ns and Formula for L = 8, δ = 0.0625, and U/thop = 5.

    fig. S4. Time dependence of double occupancy D for L = 8, δ = 0.0625, and U/thop = 5.

    fig. S5. Time dependence of peak value of charge structure factor N(qpeak = (±2π/L, 0)) for L = 8, δ = 0.0625, and U/thop = 5.

    fig. S6. Time dependence of superconducting correlations for L = 8, δ = 0.0625, and U/thop = 5.

    fig. S7. Time dependence of Formula for L = 8, δ = 0.0625, and U/thop = 5 during and after the laser irradiation.

    fig. S8. Time dependence of E/Ns and Formula for L = 8, δ ≈ 0.06, and U/thop = 5 during and after the laser irradiation.

    fig. S9. Envelop function of the laser g(t).

    Reference (42)

  • Supplementary Materials

    This PDF file includes:

    • Supplementary Text (sections SA to SC)
    • fig. S1. Superconducting correlation functions at furthest site Pd(|r| = rmax) in equilibrium and nonequilibrium obtained from the exact calculations.
    • fig. S2. Dynamics of the superconducting correlations in two-dimensional Hubbard model for L = 4 and δ = 0.25 calculated from the exact Schrӧdinger dynamics.
    • fig. S3. Time dependence of E/Ns and E/ Ns for L = 8, δ = 0.0625, and U/thop = 5.
    • fig. S4. Time dependence of double occupancy D for L = 8, δ = 0.0625, and U/thop = 5.
    • fig. S5. Time dependence of peak value of charge structure factor N(qpeak = (±2π/L, 0)) for L = 8, δ = 0.0625, and U/thop = 5.
    • fig. S6. Time dependence of superconducting correlations for L = 8, δ = 0.0625, and U/thop = 5.
    • fig. S7. Time dependence of Pd for L = 8, δ = 0.0625, and U/thop = 5 during and after the laser irradiation.
    • fig. S8. Time dependence of E/Ns and E/ Ns for L = 8, δ ≈ 0.06, and U/thop = 5 during and after the laser irradiation.
    • fig. S9. Envelop function of the laser g(t).
    • Reference (42)

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