The thermal conductivity of the heavy-fermion superconductor CeCoIn5 has been studied in a magnetic field rotating within the 2D planes. A clear fourfold symmetry of the thermal conductivity which is characteristic of a superconducting gap with nodes along the ( +/- pi,+/- pi) directions is resolved. The thermal conductivity measurement also reveals a first-order transition at H(c2), indicating a Pauli limited superconducting state. These results indicate that the symmetry most likely belongs to d(x(2)-y(2)), implying that the anisotropic antiferromagnetic fluctuation is relevant to the superconductivity.

The superconducting gap structure of recently discovered heavy fermion superconductor PrOs4Sb12 was investigated by using thermal transport measurements in magnetic field rotated relative to the crystal axes. We demonstrate that a novel change in the symmetry of the superconducting gap function occurs deep inside the superconducting state, giving a clear indication of the presence of two distinct superconducting phases with twofold and fourfold symmetries. We infer that the gap functions in both phases have a point node singularity, in contrast to the familiar line node singularity observed in almost all unconventional superconductors.

To clarify the superconducting gap structure of the spin-triplet superconductor Sr2RuO4, the in-plane thermal conductivity has been measured as a function of relative orientations of the thermal flow, the crystal axes, and a magnetic field rotating within the 2D RuO2 planes. The in-plane variation of the thermal conductivity is incompatible with any model with line nodes vertical to the 2D planes and indicates the existence of horizontal nodes. These results place strong constraints on models that attempt to explain the mechanism of the triplet superconductivity.

By performing combined resistivity and calorimetric experiments under pressure, we have determined a precise temperature-pressure ͑T , P͒ phase diagram of the heavy fermion compound URu 2 Si 2 . It will be compared with previous diagrams determined by elastic neutron diffraction and strain gauge techniques. At first glance, the low-pressure ordered phase referred to as hidden order is dominated by Fermi-surface nesting, which has strong consequences on the localized spin dynamics. The high-pressure phase is dominated by large moment antiferromagnetism ͑LMAF͒ coexisting with at least dynamical nesting needed to restore on cooling a local moment behavior. ac calorimetry confirms unambiguously that bulk superconductivity does not coexist with LMAF. URu 2 Si 2 is one of the most spectacular examples of the dual itinerant and local character of uranium-based heavy fermion compounds.

Abstract. Over the past two decades, unconventional superconductivity with gap symmetry other than s-wave has been found in several classes of materials, including heavy fermion (HF), high-T c , and organic superconductors. Unconventional superconductivity is characterized by anisotropic superconducting gap functions, which may have zeros (nodes) along certain directions in the Brillouin zone. The nodal structure is closely related to the pairing interaction, and it is widely believed that the presence of nodes is a signature of magnetic or some other exotic, rather than conventional phonon-mediated, pairing mechanism. Therefore experimental determination of the gap function is of fundamental importance. However, the detailed gap structure, especially the direction of the nodes, is an unresolved issue in most unconventional superconductors. Recently it has been demonstrated that the thermal conductivity and specific heat measurements under magnetic field rotated relative to the crystal axes are a powerful method for determining the shape of the gap and the nodal directions in the bulk. Here we review the theoretical underpinnings of the method and the results for the nodal structure of several unconventional superconductors, including borocarbide YNi 2 B 2 C, heavy fermions UPd 2 Al 3 , CeCoIn 5 , and PrOs 4 Sb 12 , organic superconductor, κ-(BEDT-TTF) 2 Cu(NCS) 2 , and ruthenate Sr 2 RuO 4 , determined by angular variation of the thermal conductivity and heat capacity.2

To determine the superconducting gap function of YNi2B2C, the c-axis thermal conductivity kappa(zz) was measured in H rotated in various directions. The angular variation of kappa(zz) in H rotated within the ab plane shows a peculiar fourfold oscillation with narrow cusps. The amplitude of this fourfold oscillation becomes very small when H is rotated conically around the c axis with a tilt angle of 45 degrees. These results provide the first compelling evidence that the gap function has point nodes located along the a and b axes. This unprecedented gap structure challenges the current view on the pairing mechanism.

The thermal conductivity of organic superconductor κ-(BEDT-TTF)2Cu(NCS)2 (Tc=10.4 K) has been studied in a magnetic field rotating within the 2D superconducting planes with high alignment precision. At low temperatures (T < ∼ 0.5 K), a clear fourfold symmetry in the angular variation, which is characteristic of a d-wave superconducting gap with nodes along the directions rotated 45 • relative to the b and c axes of the crystal, was resolved. The determined nodal structure is inconsistent with recent theoretical predictions of superconductivity induced by the antiferromagnetic spin fluctuation. 74.20.Rp, 74.25.Fy, 74.25.Jb, 74.70.Kn Since the discovery of superconductivity in organic materials about 2 decades ago, the question of the pairing symmetry among this class of materials is one of the most intriguing problems. In particular, the nature of the superconductivity in quasi-2D κ-(BEDT-TTF) 2 X salts (κ-(ET) 2 X), where the ion X can, for example, be Cu(SCN) 2 , Cu[N(CN) 2 ]Br or I 3 , has attracted considerable attention. In these layered organics, Shubnikov-de Haas oscillation experiments have established the existence of a well-defined Fermi surface (FS), demonstrating the Fermi liquid character of the low energy excitation. The large enhancement of the effective mass revealed by the specific heat as well as magnetic susceptibility measurements suggests the strong electron correlation effect in the normal state. Moreover, it was suggested that superconductivity occurs in proximity to the antiferromagnetic (AF) ordered state in the phase diagram [1]. Since some of these unusual properties suggest analogies with high-T c cuprates [2], it was pointed out by many authors that the AF spin-fluctuation should play an important role for the occurrence of superconductivity [3,4].Unconventional superconductivity is characterized by a superconducting gap with nodes along certain crystal directions. Since the superconducting gap structure is intimately related to the pairing interaction, its identification is crucial for understanding the pairing mechanism. Although the structure of the superconducting order parameter of κ-(ET) 2 X salts has been examined by several techniques, it is still controversial as we now summarize [1]. Results strongly in favor of unconventional pairing symmetry came from NMR experiments of κ-(ET) 2 Cu[N(CN) 2 ]Br, in which the absence of the Hebel-Slichter peak and cubic T -dependence of the spin lattice relaxation rate 1/T 1 were interpreted as an indication of d-wave pairing with line nodes [1,5]. The existence of the T -linear term in the thermal conductivity at low temperatures of κ-(ET) 2 Cu(NCS) 2 also supported the presence of line nodes [6]. However, some of the specific heat and penetration depth studies on these materials led to conflicting results. For example, recent specific heat measurements reported a fully gapped superconductivity [7]. Since these measurements rely on the T -dependence of the physical quantities, it is more desirable to measure the in-plane anisotropy of th...

The superconducting gap structure of recently discovered heavy fermion CePt3Si without spatial inversion symmetry was investigated by thermal transport measurements down to 40 mK. In zero field a residual T -linear term was clearly resolved as T → 0, with a magnitude in good agreement with the value expected for a residual normal fluid with a nodal gap structure, together with a T 2 -dependence at high temperatures. With an applied magnetic fields, the thermal conductivity grows rapidly, in dramatic contrast to fully gapped superconductors, and exhibits one-parameter scaling with T / √ H. These results place an important constraint on the order parameter symmetry, that is CePt3Si is most likely to have line nodes.PACS numbers: 74.20. Rp, 74.25.Bt, 74.25.Fy, 74.70.Tx @ In heavy fermion (HF) compounds containing Ce, Pr and U atoms, the strong Coulomb repulsion within the atomic f -shells leads to a notable many-body effect and often gives rise to unconventional superconductivity, in which the superconducting gap function has line or point nodes along certain directions in the Brillouin zone. Since the gap structure is closely related to the pairing mechanism of the electrons, the gap structure of HF superconductors is very important in understanding the physics of unconventional superconductivity in strongly correlated systems [1,2].Very recently a new HF superconductor CePt 3 Si with T c =0.75 K has been discovered [3]. CePt 3 Si has aroused great interest because it possesses quite unique properties. The most noticeable feature is the absence of spatial inversion symmetry, in contrast to most unconventional superconductors. It is well known that in the presence of strong spin-orbit interaction, the absence of inversion symmetry gives rise to a splitting of the two spin degenerate bands. It has been shown that the lifted spin degeneracy strongly influences the pairing symmetry of Cooper pairs [3,4,5,6,7,8,9,10,11,12]. For example, Rashba-type spin-orbit interaction dramatically changes the paramagnetic effect, which breaks up Cooper pairs [5,6,7,8,9]. According to a subsequent band structure calculation, the band splitting energy near the Fermi level in CePt 3 Si is more than a thousand times larger than k B T c , indicating strong spin-orbit coupling [10]. The special interest in the symmetry of CePt 3 Si has arisen with the observation that the upper critical field H c2 ∼ 4 T drastically exceeds the Pauli paramagnetic limit H P ∼ 1.3k B T c /µ B ∼1 T [3]. Moreover, recent NMR measurements have reported no change of the Knight shift below T c for H c [13]. These results indicate that the paramagnetic effect on Cooper pairs is absent or is strongly reduced in CePt 3 Si. Generally in the system without inversion symmetry the gap function is a mixture of spin-singlet and -triplet channels in the pres-