The gap symmetry of unconventional superconductors has attracted much attention of scientific community because it is closely related to the exotic pairing mechanism. CeCu₂Si₂ (T_c ~ 0.6 K) is a historically important compound that made a breakthrough in the field of superconductivity; in 1979, exotic superconductivity was discovered for the first time in this strongly-correlated heavy-electron system [1]. Until quite recently, its gap symmetry was believed to be a nodal d-wave pairing mediated by spin fluctuations [2]. The presence of line nodes had been suggested from the power-law temperature dependence of various physical quantities, such as the NMR relaxation rate 1/T₁ [3] and the specific heat, both of which were measured in the intermediate temperature region above 0.1 K. Recent interest has been focused on the location of line nodes: whether the gap symmetry is d_x2−y2 or d_xy type [4,5].

Fig. 1. (a) Temperature dependence of the electronic specific heat of CeCu₂Si₂ divided by temperature, C_e /T, for H // [100]. (b) Temperature dependence of C_e /T at zero field, where the T-dependent normal-state contribution is subtracted. The solid line is a best fit to the two-gap BCS model. (c) Field-temperature phase diagram for H // [100] and a contour plot of the superconducting contribution to C_e /T. Anomalous behavior that can be ascribed to the Pauli paramagnetic effect is clearly seen in the high-field and low-temperature region below 0.1 K.

Fig. 2. The calculated Fermi surfaces of CeCu₂Si₂ colored by the magnitude of the Fermi velocity ν_F.

To elucidate the gap symmetry of CeCu₂Si₂, we performed specific-heat measurements at low temperatures down to 40 mK using a high-quality single crystal (S-type)[6]. Quite unexpectedly, the zero-field specific heat C_e exhibits exponential temperature dependence below 80 mK (Fig. 1(a)), reminiscent of full-gap superconductivity. In addition, we provide thermodynamic evidence for nodeless superconductivity that the low-temperature specific heat is proportional to the magnetic field at low fields for all field orientations and does not change with the c-plane field rotation. We found that the temperature dependence of the zero-field C_e /T including the linear behavior in the intermediate-T region can be reproduced on the basis of a phenomenological two-gap model within the conventional BCS framework using two BCS gaps, Δ₁ = 1.76k_BT_c and Δ₂ = 0.7k_BT_c, whose weights are 65% and 35% of the total density of states, respectively (Fig. 1(b)). We also found anomalous behaviors in the field variations of the specific heat as well as the magnetization at low temperatures in the high-field regime (Fig. 1(c)), which can be interpreted as a strong Pauli paramagnetic effect occurring in a multiband superconductor. All the present results match with the prediction of multiband superconductivity in the absence of nodal quasiparticles.

One may suspect that line nodes might exist in the gap on light-mass bands, since the specific heat measurement mainly probes the heavy-mass band. To get an insight into the band structure of CeCu₂Si₂, we have performed first-principles calculations by the LDA+U method. As shown in Fig. 2, CeCu₂Si₂ has a flat electron band around the X point with the heaviest mass and two hole bands around the Z point. In this Fermi-surface topology, the deficiency of nodal quasiparticles requires the negligibly small effective mass of the two light-mass bands, which contradicts the multiband feature detected from the specific-heat measurement. This leads to a conclusion that the pairing symmetry of CeCu₂Si₂ is not the anticipated d-wave state, but the multiband full-gap state, including an unconventional s-wave such as s±-wave, a conventional s-wave, or a fully-gapped d+id state. These findings would open a new door into electron pairing in CeCu₂Si₂ and help understand the pairing mechanism of exotic superconductors.

References

• [1] F. Steglich et al., Phys. Rev. Lett. 43, 1892 (1979).
• [2] O. Stockert et al., Nat. Phys. 7, 119 (2011).
• [3] Y. Kitaoka et al., J. Phys. Soc. Jpn. 55, 723 (1986).
• [4] H. A. Vieyra et al., Phys. Rev. Lett. 106, 207001 (2011).
• [5] I. Eremin et al., Phys. Rev. Lett. 101, 187001 (2008).
• [6] S. Kittaka et al., Phys. Rev. Lett. 112, 067002 (2014).

Authors

• S. Kittaka, Y. Aoki, Y. Shimura, T. Sakakibara, S. Seiro^a, C. Geibel^a, F. Steglich^a, H. Ikeda^b, K. Machida^c
• ^aMax-Planck-Institute for Chemical Physics of Solids
• ^bKyoto University
• ^cOkayama University