Research ArticlePHYSICS

Fully gapped superconductivity with no sign change in the prototypical heavy-fermion CeCu2Si2

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Science Advances  23 Jun 2017:
Vol. 3, no. 6, e1601667
DOI: 10.1126/sciadv.1601667
  • Fig. 1 Pairing interactions and superconducting gap functions.

    (A) Pairing interaction in real space for attractive force mediated by electron-phonon interaction. Blue part corresponds to attractive region. Both electrons composing the Cooper pair can occupy the same atom. (B) Isotropic s-wave superconducting state in the momentum space driven by the attractive force shown in (A). The gap function is constant in the entire Brillouin zone. (C) Pairing interaction due to magnetic fluctuations. The red and blue parts correspond to repulsive and attractive regions, respectively. Both electrons cannot occupy the same atom. Superconductivity is caused by the attractive part of the oscillating pairing interaction. (D and E) Examples for the gap structures in momentum space for unconventional superconductors caused by an on-site repulsive force, Embedded Image symmetry (D), and s± symmetry (E). Because of the sign change of the superconducting order parameter, the gap vanishes on the yellow lines. When the Fermi surface crosses these lines, gap nodes appear.

  • Fig. 2 Phase diagrams and electronic structure of CeCu2Si2.

    (A) Schematic T-g phase diagram, where g is a nonthermal control parameter, such as pressure, substitution, or Cu deficiency. Red and blue arrows indicate two different types of CeCu2Si2 with antiferromagnetic (A-type) and superconducting (S-type) ground states, respectively. The S-type crystal locates very close to antiferromagnetic (AFM) QCP. (B) Fermi surface colored by the Fermi velocity (in units of 106 m/s) obtained by the local density approximation (LDA) + U calculation (12). Fermi surface consists of separated electron and hole pockets: heavy electron pockets with cylindrical shape around X-point and rather complicated light hole pockets centered at Γ point. (C) H-T phase diagram with color coding of T exponent (ϵ) of the in-plane electrical resistivity, ρ(T) = ρ0 + ATϵ for Hc. Inset shows the T dependence of ρ(T) in zero field and in magnetic fields of 2.5 and 12 T applied along the c axis.

  • Fig. 3 Temperature dependencies of specific heat and London penetration depth well below the superconducting transition temperature Tc.

    (A) Inset shows the specific heat divided by temperature C/T in zero field and in the normal state at μ0H = 2 T for Hab plane. The main panel shows C/T at low temperatures. The gray solid line is an exponential fit of the data, yielding Δ = 0.39 K. (B) Temperature-dependent change in the in-plane penetration depth Δλ in a single crystal of CeCu2Si2. The dashed (solid) line is a fit to a power law (exponential) temperature dependence up to 0.2 K. Inset shows the normalized superfluid density ρs(T) = λ2(0)/λ2(T) as a function of T/Tc, extracted by using a value of λ(0) = 700 nm (section S2). The dashed line is the temperature dependence of ρs(T) in the simple d-wave case.

  • Fig. 4 Thermal conductivity of CeCu2Si2 for various directions of thermal current and magnetic field.

    (A) Temperature dependence of the in-plane thermal conductivity divided by temperature κa/T in zero field and in magnetic field of μ0H = 2.2 T applied along the c axis. WF refers to κ/T at T → 0 calculated from the Wiedemann-Franz law. (B) Field dependence of κ/T for two different configurations: (i) κa/T (Qa) in Hc and (ii) κc/T (Qc) in Hc. In these configurations, thermal conductivity selectively probes the excited quasi-particles with in-plane momentum. The dashed horizontal lines represent the phonon contribution, κph/T, estimated from the WF law above upper critical field (see the main text). (C) Field dependence of κc/T for configuration (iii), where Qc and Ha. In this case, thermal conductivity selectively probes the excited quasi-particles with out-of-plane momentum. (D) Field-induced enhancement of thermal conductivity Δκ(H) ≡ κ(H) − κ(0) normalized by the normal-state value, Δκ(H)/Δκ(Hc2), for the configurations (i), (ii), and (iii) plotted against the magnetic field normalized by the upper critical fields. Black and green broken lines represent the field dependencies expected for line and point nodes.

  • Fig. 5 Pair-breaking effect of CeCu2Si2.

    (A) Suppression of superconducting transition temperature Tc/Tc0 as a function of ρ0/Tc0, which is proportional to the pair-breaking parameter for CeCu2Si2 and Sn-substituted CeCoIn5 (d-wave) (30). Here, Tc0 is the transition temperature with no pair-breaking effect and ρ0 is the residual resistivity. For CeCu2Si2, Tc0 = 0.71 K is used. Inset shows the temperature dependence of resistivity in CeCu2Si2 before and after electron irradiation, which creates point defects. (B) Comparison of impurity effect of CeCu2Si2 with those of other superconductors. Suppression of superconducting transition temperature Tc/Tc0 as a function of dimensionless pair-breaking parameter ℏ︀/τimpkBTc0. The solid line shows the prediction of the Abrikosov-Gor’kov (AG) theory for an isotropic s-wave superconductor with magnetic impurities. We also plot the data for Sn-substituted CeCoIn5 (d-wave) (30), electron-irradiated YBa2Cu3O7-δ (d-wave) (31), electron-irradiated Ba(Fe0.76Ru0.24)2As2 (possibly s± wave) (32), and neutron-irradiated MgB2 (33) and YNi2B2C (35). The value of Tc0 is estimated by extrapolating two initial data points to zero 1/τimp limit. Rather weak pair-breaking effect in Ba(Fe0.76Ru0.24)2As2 has been attributed to a large imbalance between intra- and interband scattering (32). For MgB2 data, we use the value of λab(0) = λc(0) = 100 nm (34). For YNi2B2C data, we use λab(0) = 110 nm (36) and Embedded Image nm (37), where Embedded Image and Embedded Image are upper critical fields parallel and perpendicular to the ab plane.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/3/6/e1601667/DC1

    section S1. Temperature dependence of penetration depth

    section S2. Lower critical field

    section S3. Zero-field thermal conductivity

    fig. S1. Magnetic penetration depth versus temperature for two samples measured.

    fig. S2. Parameters obtained for the fits to the Δλ(T) data.

    fig. S3. Lower–critical field measurements of CeCu2Si2.

    fig. S4. Temperature dependence of thermal conductivity at low temperatures.

    References (5254)

  • Supplementary Materials

    This PDF file includes:

    • section S1. Temperature dependence of penetration depth
    • section S2. Lower critical field
    • section S3. Zero-field thermal conductivity
    • fig. S1. Magnetic penetration depth versus temperature for two samples measured.
    • fig. S2. Parameters obtained for the fits to the Δλ(T) data.
    • fig. S3. Lower–critical field measurements of CeCu2Si2.
    • fig. S4. Temperature dependence of thermal conductivity at low temperatures.
    • References (52–54)

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