Theory of a new type of heavy-electron superconductivity in PrOs₄Sb₁₂: quadrupolar-fluctuation mediated odd-parity pairings

Abstract

It is shown that unconventional nature of superconducting state of PrOs 4 Sb 12 , a Pr-based heavy electron compound with the filled-Skutterudite structure, can be explained in a unified way by taking into account the structure of the crystallineelectric-field (CEF) level, the shape of the Fermi surface determined by the band structure calculation, and a picture of the quasiparticles in f 2 -configuration with magnetically singlet CEF ground state. Possible types of pairing are narrowed down by consulting recent experimental results. In particular, the chiral "p"-wave states such as p x + ip y is favoured under the magnetic field due to the orbital Zeeman effect, while the "p"-wave states with two-fold symmetery such as p x can be stabilized by a feedback effect without the magnetic field. It is also discussed that the double superconducting transition without the magnetic field is possible due to the spin-orbit coupling of the "triplet" Cooper pairs in the chiral state.Recently, the superconductivity has been found in heavy electron compound PrOs 4 Sb 12 with the crystal structure of the filled Skutterudite [1]. Since the specific heat jump ∆C at the superconducting transition temperature T c =1.8K is quite enhanced as ∆C/T c ≃ 500 mJ/K 2 mole, heavy quasiparticles are responsible for the Cooper pair formation. Quite recently, a measurement of the longitudinal relaxation rate, 1/T 1 , of NQR at Sb site has been performed and very unusual temperature (T ) dependence was revealed both for T < T c and T > T c [2], while the normal state properties had been known to be also quite unconventional [1,3]. Unconventional behaviors of 1/T 1 are summarized as follows: 1) Pseudo gap behavior is seen in 1/T 1 T at T c < T < 2T c , in which the resistivity ρ also shows a pseudo-gap behavior [1]. 2) There is no trace of the coherence (Hebel-Slichter) peak around T = T c at all. 3) 1/T 1 appears to exhibit an exponential T -dependence below 1.3T c , giving the superconducting gap ∆ in the low temperature limit as 2∆/k B T c ≃ 5.3, although a possibility is not ruled out that the crossover to the T 3 -dependence begins to be observed at around T ≃ T c /3 the lowest temperature covered by experiments.Very recently, the anomaly of specific heat near T c has been observed, which suggests a double transition at T = T c1 and T c2 (T c2 < T c1 ) [3,4] It also turned out very recently on the basis of measurements of the angular dependence of the thermal conductivity κ under the magnetic field H [5] that there exsist at least two different superconducting phases in the T -H phase diagram. In the low-field phase, the 2-fold component of κ z along the z-direction is observed as a function of the angle of the direction of H around the z-axis, while the 4-fold one is observed in the high-field phase. The phase boundary approaches the lower critical temperature T c2 as H → 0. This is in marked contrast with the case of a heavy electron superconductor CeCoIn 5 where the data can be interpreted by a simple "d"-wave model [6]. These behaviors s...

Superconducting phase diagram of the filled skuterruditePrOs4Sb12

“…Even for a weak coupling picture (λ = 0.6), the fit yields g = 1.55. In both cases, the paramagnetic limit remains important, supporting a singlet nature of the superconductivity, contrary to that had been suggested in 37,38,39 and in agreement with the supposition in 7,29 . This result should be quite robust, independent of the two band model.…”

Field-dependent mass enhancement inPr1−xLaxOs4Sb12Zwicknagl1, Thalmeier2, Fulde3 2009Phys. Rev. B11180View full textAdd to dashboardCite

“…Aside from subtle effects this is quite similar to the LDA FS in Ref. 17 (note that in this reference the FS is depicted in the hole picture as in Fig. 1a).…”

Recent Advances in the Magnetism and Superconductivity of Heavy Fermion Systems

“…103) These results might indicate an oddparity pairing based on the quadrupole fluctuations. 104) As noted in the previous section, it was clarified that superconductivity truly coexists with strong ferromagnetism: a magnetic moment s ¼ 1:0 B /U at 1.2 GPa in UGe 2 , as shown in Fig. 20.…”