Research ArticleMATERIALS SCIENCE

Energy gap evolution across the superconductivity dome in single crystals of (Ba1−xKx)Fe2As2

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Science Advances  30 Sep 2016:
Vol. 2, no. 9, e1600807
DOI: 10.1126/sciadv.1600807
  • Fig. 1 (Color online) Schematic illustration of the effective band structure and order parameter evolution with doping.

    (A) Change in the electronic band structure across the Lifshitz transition. The electron pocket at M is lifted but remains in the vicinity of EF. The extended s± pairing survives but is shifted to the hole bands at the Γ point. (B) Hole and electron pockets relevant for calculations with the sign-changing order parameter. Signs are encoded by green (+) and red (−) colors.

  • Fig. 2 (Color online) Temperature-composition phase diagram.

    (A) Composition-dependent superconducting transition temperature, Tc(x), in pristine (squares) and electron-irradiated (other symbols, see legend) samples. SDW, spin-density wave; SC, superconducting phase. (B) Normalized ΔTc/Tc0. The largest Tc suppression is found at x ≳ 0.8. The color shade indicates long-range magnetic order at small x and crossover to nodal behavior at large x.

  • Fig. 3 (Color online) Normalized suppression, ΔTc/Tc0 versus resistivity at Tc obtained from normal skin depth (see fig. S2).
  • Fig. 4 (Color online) Evolution of temperature dependence of London penetration depth (Δλ).

    Upper panels: Δ(T/Tc) for 16 different compositions before and after electron irradiation. Each individual panel shows a low-temperature region of T/Tc < 0.3 (full-range curves are shown in fig. S1). Lower panels: Exponent n obtained from the power-law fitting, Δλ = A(T/Tc)n. For each curve, three different upper-limit temperatures were used, Tup/Tc = 0.20, 0.25, and 0.30, whereas the lower limit was fixed by the lowest temperature.

  • Fig. 5 (Color online) Absolute change of Δλ from 0 to 0.3Tc for all compositions.

    (A) The change in the London penetration depth, Δλ (0.3Tc), versus x for pristine and postirradiated samples. (B) Composition dependence of the power-law exponent n for pristine and irradiated samples. As the irradiation dose increases, the exponent approaches, but never exceeds the value of n = 2.

  • Fig. 6 (Color online) Evolution of the superconducting gaps in BaK122 with composition, x, obtained from self-consistent t-matrix fitting (see fig. S3) as described in the text.

    Assumed angular variations of the gaps is shown schematically in Fig. 1. As long as the isotropic part is greater than the anisotropic one, the state is nodeless (that is, for x < 0.8). In the opposite limit, the nodes appear. This is shown by inscribed triangles in the figure for h1 contribution. Consequently, the s± pairing switches from hole-electron pockets below the Lifshitz transition to hole-hole above.

  • Fig. 7 (Color online) The change in penetration depth for the x > 0.9 samples fitted with symmetry-imposed d-wave and s± states.

    For d-wave fit, both the hole bands are assumed to have gaps of the Embedded Image form. The gap magnitudes (Δ01, Δ02) for dopings x = 0.91, 0.92, and 1.00 are (1.5,1.8), (1.6,1.2), and (1.0,1.2), respectively, in units of Tc.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/2/9/e1600807/DC1

    London penetration depth

    T-matrix fitting procedure

    fig. S1. (Color online) Full transition curves of Δλ(T) for the studied samples.

    fig. S2. (Color online) Resistivity estimated from the skin depth (TDR).

    fig. S3. (Color online) t-Matrix fitting of the London penetration depth for compositions spanning the superconductivity dome.

    fig. S4. (Color online) Variation of superconducting critical temperature upon irradiation for different compositions.

    fig. S5. (Color online) Comparison of Tc suppression as a function of increasing disorder for various possible scenarios for heavily overdoped systems.

  • Supplementary Materials

    This PDF file includes:

    • London penetration depth
    • T-matrix fitting procedure
    • fig. S1. (Color online) Full transition curves of Δλ(T) for the studied samples.
    • fig. S2. (Color online) Resistivity estimated from the skin depth (TDR).
    • fig. S3. (Color online) t-Matrix fitting of the London penetration depth for compositions spanning the superconductivity dome.
    • fig. S4. (Color online) Variation of superconducting critical temperature upon irradiation for different compositions.
    • fig. S5. (Color online) Comparison of Tc suppression as a function of increasing disorder for various possible scenarios for heavily overdoped systems.

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