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Sign-Reversal of Field-Angle Resolved Specific Heat Oscillations in a Heavy Fermion Superconductor CeCoIn5 and kx2-ky2 Pairing Symmetry

Sakakibara Group

Heavy-electron superconductors mostly have anisotropic gap functions which vanish (have nodes) for certain directions in the momentum space. Since the nodal structure is closely related to the pairing mechanism, its experimental determination is very important. To identify the gap structure is, however, a formidable task. Here we address the directional thermodynamic measurements. In anisotropic superconductors, low energy spectrum of the quasiparticles in the vortex state much depends on the nodal structure. In particular, the electronic specific heat (C) has been demonstrated to exhibit a characteristic dependence on the angle between the field and the nodal directions [1]; in a low temperature "semiclassical" regime, C takes maxima (minima) when a magnetic field H is oriented along the antinodal (nodal) directions. This effect allows one to probe the nodal structures experimentally. We have been investigating the anisotropic gap structures of heavy-electron superconductors by means of field-angle dependent specific heat (Cθ) measurements [2].

Fig.1. Contour plot of the fourfold amplitude A4(T,H) of CeCoIn5 obtained by the field-angle resolved specific heat (Cθ) measurements. In the high-T and high-H (blue colored) region, Cθ takes minima along the aninodal ([100]) directions. On entering the semiclassical region bounded by the dashed line, Cθ changes the sign of the oscillation and takes minima along the nodal ([110]) directions. From these observations, the gap symmetry of CeCoIn5 was confirmed to be kx2-ky2.

In the heavy fermion superconductor CeCoIn5 (Tc=2.3 K), our previous Cθ measurements (Hc) performed down to 300 mK (T/Tc=0.13) revealed a clear fourfold oscillation with minima along [100] directions [3]. A naive interpretation of the results infers that the nodal direction is [100] (kxky symmetry), which is contrary to other various experiments on CeCoIn5 including the field-orientation dependent thermal conductivity measurements [4] where kx2-ky2 symmetry is deduced. Very recently, Cθ of d-wave superconductors has been studied theoretically in a wide H-T region [5]. It has been pointed out that applying H along the gap nodes may result in maxima of Cθ in an intermediate-T region. That is, the anisotropy of Cθ changes sign at a low temperature T/Tc~0.1 [5]. If this would be the case for CeCoIn5, then our previous Cθ data would be interpreted in terms of kx2-ky2 symmetry. In order to explore this possibility, we extended the Cθ measurements on CeCoIn5 to lower T down to 120 mK using a dilution refrigerator [6]. The magnetic field was rotated in the ab plane, covering from [100] through [010] directions.

We observed a fourfold angular oscillation of Cθ which can be expressed in a form C=C0)+CH(1-A4cos4θ), where C0 and CH denote the field independent and dependent part of the specific heat, respectively, and θ is the angle of H measured from the [100] direction. Figure 1 shows a contour plot of the observed fourfold amplitude A4 in the H-T plane, where H and T are reduced by Hc2=11.5 T and Tc. In a blue-colored region, A4 is positive and Cθ takes minima along [100] directions, in full agreement with our previous experiment [3]. On cooling below 200 mK, we did observe a sign change in A4 as shown in the figure. The sign reversal in A4 is observed only at very low fields (H≤0.15Hc2). The crossover temperature of the sign reversal well agrees with the theoretical prediction, indicating that, for the first time, the low-temperature semiclassical region is reached experimentally [6]. In this region, Cθ takes minima along the [110] nodal directions, implying unambiguously that the gap symmetry of CeCoIn5 is kx2-ky2.


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Authors
  • b Okayama University
  • a Osaka University
  • K. An, T. Sakakibara, R. Settaia, Y. Onukia, M. Hiragib, M. Ichiokab, and K. Machidab