Anomalous Field-Angle Dependence of the Specific Heat of Heavy-Fermion Superconductor UPt₃

Abstract

We have investigated the field-angle variation of the specific heat C(H, φ, θ) of the heavy-fermion superconductor UPt 3 at low temperatures T down to 50 mK, where φ and θ denote the azimuthal and polar angles of the magnetic field H, respectively. For T = 88 mK, C(H, θ = 90• ) increases proportionally to √ H up to nearly the upper critical field H c2 , indicating the presence of line nodes. By contrast, C(H, θ = 0 • ) deviates upward from the √ H dependence for √ H/H c2 0.5. This behavior can be related to the suppression of H c2 along the c direction, whose origin has not been resolved yet. Our data show that the unusual H c2 limit becomes marked only when θ is smaller than 30• . In order to explore the possible vertical line nodes in the gap structure, we measured the φ dependence of C in wide T and H ranges. However, we did not observe any in-plane angular oscillation of C within the accuracy of ∆C/C ∼ 0.5%. This result implies that field-induced excitations of the heavy quasiparticles occur isotropically with respect to φ, which is apparently contrary to the recent finding of a twofold thermal-conductivity κ(φ) oscillation.

Exotic Multigap Structure in UPt3 Unveiled by a First-Principles Analysis

“…Since the relevant FS has a large DOS, the in-plane twofold oscillation should be detected also in any experimental observations. However, this is incompatible with the observation in the field-angle resolved specific heat measurement [26].…”

“…This strongly promoted the field-angle resolved specific heat measurement. However, the complimentary measurements have not detected any signature of in-plane symmetry breaking in any phases [26]. Although this seems to contradict the result in the thermal conductivity, it is expected to be explained by considering the multi-band nature of UPt 3 .…”

“…Since the relevant FS has a large DOS, the in-plane twofold oscillation should be detected also in any experimental observations. However, this is incompatible with the observation in the field-angle resolved specific heat measurement [26].Furthermore, let us consider the gap structure in the E 2u state in Figs.4(d)-(f). Surprisingly, we find that the nodal feature is completely different on each FS; a horizontal nodes in Fig.4(d), point nodes at the top of FS in Fig.4(e), and in-plane twofold vertical line nodes in Fig.4(f).…”

“…Such peculiar feature cannot be explained in the conventional pseudo-spin representation, but is described 5 by the group-theoretical representation of the Cooper pairs in the j = 5/2 space. Furthermore, the study of magnetic anisotropy and the mixture of p-wave and fwave with different d-vectors can provide a clue to understand the remaining problems of the Pauli limiting of the upper critical field [17,26,54] and the anomalous behavior of the Knight shift [55] and so on. These are interesting issues in future, together with the understanding of the multiple superconducting phases.…”

Surface State Tunneling Signatures in the Two-Component Superconductor UPt3

“…Both model gap functions have similar nodal structure: A line node in the hexagonal ab symmetry plane and two point nodes at the poles on the k z -axis which are of first (E 1g ) or second (E 2u ) order. More recently as a result of thermal conductivity [19][20][21] and specific heat [22] measurements in rotating magnetic field a revision to a triplet E 1u model was controversially discussed. It has again first order point nodes at the poles but node lines are located in two off-symmetry planes parallel to hexagonal ab plane.…”