Research ArticleCONDENSED MATTER PHYSICS

Strong coupling superconductivity in a quasiperiodic host-guest structure

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Science Advances  13 Apr 2018:
Vol. 4, no. 4, eaao4793
DOI: 10.1126/sciadv.aao4793
  • Fig. 1 Evolution of the temperature dependence of the resistivity ρ(T) of bismuth with pressure p.

    As p approaches 25 kbar, ρ rises rapidly at low T, indicating a reduction in the carrier concentration. Over a narrow range in p and T above 25 kbar, Bi is known to assume the Bi-II structure (blue line), which goes along with a drastic decrease in ρ(300 K). At higher pressures still, Bi orders in the incommensurate Bi-III structure (red line). (Inset) Crystal structure of Bi-I and schematic p-T phase diagram of Bi.

  • Fig. 2 ρ(T) for bismuth at 27 kbar (Bi-III), showing a nearly linear T dependence at low T above a superconducting transition at Tc ≃ 7.05 K.

    Moderate magnetic fields (1, 2, and 3 T) suppress Tc, but the critical field ≃ 2.5 T is much higher than that of Pb, which has a similar Tc ≃ 7.2 K but a far weaker T dependence of ρ(T) (black line). Left inset: Crystal structure of Bi-III, showing the commensurate arrangement within the ab plane of guest (purple) and host atoms (gray). Along the c axis (right inset), the discrepancy between the lattice constants of guest and host atoms becomes apparent.

  • Fig. 3 Low T resistivity of bismuth at 31.4 kbar in 0.5 T field increments from 0 to 3 T.

    Inset: Upper critical field Bc2 for Bi-III at 31.4 kbar (full symbols) and 27 kbar (empty symbols), extracted from the mid-point of the resistive transition. The measured data deviate strongly from the weak coupling clean limit Werthamer-Helfand-Hohenberg (WHH) form (18) (black line), suggesting a strong coupling description (19) (red line for λ = 2.9).

  • Fig. 4 Magnetic and phonon properties of Bi-III.

    Left: Magnetization M over applied field H (both in SI units) in Bi at 29 kbar as a function of temperature for μ0H = 0.002 T, on warming zero-field cooling (zfc) and field cooling (fc). Right: Phonon dispersion computed for wave vectors q perpendicular to c indicated by open circles, interpolated in between. We identify not only three acoustic modes (dotted lines) and a spaghetti of optical modes but also two further modes at very low energy, which have low dispersion (dashed lines). These correspond to the zero-frequency phason modes expected in the incommensurate structure of Bi-III.

  • Table 1 Experimental and calculated material parameters in Bi-III and in the reference materials In5Bi3 and Ca3Rh4Sn13 (see text).

    The coherence length ξexp is obtained from the upper critical field and can be compared to ξcalc = vF/(πΔ). The Fermi velocity vF is estimated by scaling the density functional theory (DFT) estimate Embedded Image by (1 + λρ)−1, where λρ, the electron-phonon coupling constant obtained from the slope of ρ(T) with the help of a DFT estimate of the plasma frequency Ωp (see text), is listed separately. In In5Bi3 and Ca3Rh4Sn13, it can be compared to the ratio of measured and calculated Sommerfeld coefficients λC = γexpDFT−1. In Bi-III, no heat capacity data are as yet available. The gap size 2Δ = ηkBTc with η = 5.7 for Ca3Rh4Sn13 (27) and values ≃ 5 and 4 assumed for Bi-III and In5Bi3 (Supplementary Materials). n/a, not applicable.

    Tc
    (K)
    Bc2
    (T)
    ξexp
    (Å)
    ξcalc
    (Å)
    Ωp
    (eV)
    λρλC
    Bi-III7.052.451161723.52.75n/a
    In5Bi34.140.33315002.51.250.90
    Ca3Rh4Sn138.04.0911262.21.10.80

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/4/4/eaao4793/DC1

    section S1. Material parameters from DFT

    section S2. Characterization of bismuth crystal

    section S3. Bc1 from high-pressure magnetization data

    fig. S1. Comparison between Bi-III approximants.

    fig. S2. Results of DFT calculations in Bi-III, including electronic density of states, plasma frequencies, and phonon density of states.

    fig. S3. Experimental observations in the reference material In5Bi3.

    fig. S4. X-ray characterization of bismuth sample.

    fig. S5. Extracting estimates of the lower critical field from high-pressure zero field–cooled magnetization measurements in Bi-III.

    References (5054)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Material parameters from DFT
    • section S2. Characterization of bismuth crystal
    • section S3. Bc1 from high-pressure magnetization data
    • fig. S1. Comparison between Bi-III approximants.
    • fig. S2. Results of DFT calculations in Bi-III, including electronic density of states, plasma frequencies, and phonon density of states.
    • fig. S3. Experimental observations in the reference material In5Bi3.
    • fig. S4. X-ray characterization of bismuth sample.
    • fig. S5. Extracting estimates of the lower critical field from high-pressure zero field–cooled magnetization measurements in Bi-III.
    • References (50–54)

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