Research ArticleSUPERCONDUCTORS

Unified understanding of superconductivity and Mott transition in alkali-doped fullerides from first principles

See allHide authors and affiliations

Science Advances  21 Aug 2015:
Vol. 1, no. 7, e1500568
DOI: 10.1126/sciadv.1500568
  • Fig. 1 Band structure of fcc Cs3C60 with Embedded Image.

    The blue dotted curves represent the Wannier-interpolated band dispersion calculated from Embedded Image in Eq. 1.

  • Fig. 2 Theoretical and experimental phase diagrams.

    (A) Phase diagram as a function of volume per C60 molecule and temperature, obtained with the DFT + E-DMFT. PM, PI, and SC denote the paramagnetic metal, the paramagnetic insulator, and the superconducting phase, respectively. Metallic and insulating E-DMFT solutions coexist between the blue solid line Vc2(T) and the black dotted line Vc1(T). The error bars for Tc originate from the statistical errors in the superconducting order parameters calculated with the quantum Monte Carlo method (see Section E in the Supplementary Materials for details). The error bars for Vc1(T) and Vc2(T) are half the interval of the volume grid in the calculation. (B) For comparison, the experimental phase diagram [adapted by Y. Kasahara from Figure 6 in Zadik et al. (9)] is shown, where the region depicted in (A) corresponds to the area surrounded by the green dotted lines. AFI denotes the antiferromagnetic insulator.

  • Fig. 3 Frequency dependence of effective onsite interactions.

    The effective intra- and interorbital interactions (Ueff = U + UV + Uph and Ueff = U′ + UV + Uph, respectively) consist of the constrained random-phase approximation (cRPA) onsite Coulomb repulsion (U, U′), the dynamical screening from the off-site interactions (UV = UV), and the phonon-mediated interactions (Uph, Uph). The data are calculated for Cs3C60 with Embedded Image at 40 K. We assume the cRPA Coulomb interactions to be static, whose validity is substantiated in Section B in the Supplementary Materials. Inset: Frequency dependence of Ueff and Ueff along the Matsubara frequency axis.

  • Fig. 4 Double occupancy, size of spin, weights of intramolecular configurations, spectral functions at 40 K, and schematic pictures of representative intramolecular configurations.

    (A) Volume dependence of the double-occupancy D = 〈nini〉 (red), the interorbital interspin correlation 〈ninj〉 (green), and the size S of the spin per molecule (blue). (B) Spectral functions of several fcc A3C60 systems at 40 K. For comparison, we show the DFT density of states for fcc K3C60 (Embedded Image = 722 Å3) as the shaded area. (C) Weights of several onsite configurations appearing in the quantum Monte Carlo simulations. (210) [(111)] generically denotes the configurations of {n1,n2,n3} = {2,1,0}, {0,2,1}, {1,0,2}, {2,0,1}, {1,2,0}, {0,1,2} [{n1,n2,n3} = {1,1,1}], with ni being the occupation of orbital i. N ≠ 3 with N = n1 + n2 + n3 denotes the configurations away from half filling. (D) Illustrative pictures for the (111) and (210) configurations. The up and down arrows indicate the up- and down-spin electrons, respectively.

  • Table 1 Material dependence of the static part of the phonon-mediated interactions.

    Uph(0), Uph(0), and Jph(0) are the phonon-mediated onsite intraorbital, interorbital, and exchange interaction strengths between the t1u electrons at ω = 0 calculated with the cDFPT. The energy unit is eV. The numbers just after the material names denote the volume occupied per C603− anion in Å3.

    Uph(0)Uph(0)Jph(0)
    K3C60 (722)−0.15−0.053−0.050
    Rb3C60 (750)−0.14−0.042−0.051
    Cs3C60 (762)−0.11−0.013−0.051
    Cs3C60 (784)−0.12−0.022−0.051
    Cs3C60 (804)−0.13−0.031−0.052

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/1/7/e1500568/DC1

    Text (Sections A to F)

    Fig. S1. Frequency dependence of partially screened Coulomb interactions for fcc Cs3C60 with Formula = 762 Å3.

    Fig. S2. Frequency dependence of the superconducting gap function at 10 K.

    Table S1. Summary of input parameters for the E-DMFT calculations.

    Table S2. Stability of superconducting (SC) solution at 10 K.

    References (3349)

  • Supplementary Materials

    This PDF file includes:

    • Text (Sections A to F)
    • Fig. S1. Frequency dependence of partially screened Coulomb interactions for fcc Cs3C60 with Vc3-60 = 762 Å3.
    • Fig. S2. Frequency dependence of the superconducting gap function at 10 K.
    • Table S1. Summary of input parameters for the E-DMFT calculations.
    • Table S2. Stability of superconducting (SC) solution at 10 K.
    • References (33–49)

    Download PDF

    Files in this Data Supplement:

Navigate This Article