Gap symmetry of superconductivity in UPd2Al3

Won, Hyung Jin; Parker, David; Maki, Kazumi; Watanabe, T.; Izawa, K.; Matsuda, Yoshinobu

doi:10.1103/physrevb.70.140509

Cited by 17 publications

(23 citation statements)

References 19 publications

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“…2 The magneto-thermal conductivity for these models has been calculated by the method of the Doppler shift of the energy of quasiparticles due to the circulating supercurrent flow of the vortices. 3,4 This effect depends sensitively on the angle between H and the direction of the nodes of the gap. Comparison of these Doppler shift results with the data indicates that the model type IV, ∆(k) = ∆ cos 2χ , gives the most consistent description of the experiments of Ref.…”

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Thermal conductivity in the vortex state of the superconductorUPd2Al3

Tewordt

Fay

2005

Phys. Rev. B

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The magneto-thermal conductivity κ is calculated for the vortex state of UPd2Al3 by assuming horizontal gap nodes. The Green's function method we employed takes into account the effects of supercurrent flow and Andreev scattering on the quasiparticles due to Abrikosov's vortex lattice order parameter. The calculated angular dependence of κyy for field rotation θ0 in the ac-plane depends strongly on field strength H , impurity scattering, anisotropy of the Fermi velocity, and temperature. For finite temperatures and the clean unitary scattering limit we get qualitative agreement with recent experiments for all four proposed gap functions having horizontal line nodes at c kz = 0 , ±π/4 , and ±π/2 .Angle-dependent magneto-thermal conductivity is a powerful tool for determining the nodal structure of the gap in unconventional superconductors. Recently, the thermal conductivity has been measured in the heavy-Fermion superconductor UPd 2 Al 3 for a variety of magnetic field orientations. 1 The thermal conductivity κ yy displays two-fold oscillations when the magnetic field H is rotated in the ac-plane, while no oscillations are observed when H is rotated within the basal ab-plane. These results provide strong evidence that the gap function ∆(k) has horizontal line nodes orthogonal to the c-axis. Four gap models have been proposed and denoted in Ref. 1 as types I -IV, respectively: ∆(k) ∝ sin χ , cos χ , sin 2χ , and cos 2χ (with χ = ck z ). Cooper pairing mediated by magnetic excitons yields the highest T c for the model cos χ . 2 The magneto-thermal conductivity for these models has been calculated by the method of the Doppler shift of the energy of quasiparticles due to the circulating supercurrent flow of the vortices. The purpose of the present paper is to calculate the magneto-thermal conductivity for horizontal gap nodes by another method which takes into account, beside the effect of the supercurrent flow, the Andreev scattering off the vortex cores. 5 These effects are calculated from the real and imaginary parts of the Andreev scattering self energy for the quasiparticle Green's function in the presence of Abrikosov's vortex lattice order parameter. This method was applied to Sr 2 RuO 4 by assuming vertical and horizontal nodes of the superconducting gap. 6 An equivalent method based on the quasiclassical equations and linear response theory 7 provides much more compact expressions for the density of states and thermal conductivity. 8 We have shown that the latter expressions yield very nearly the same results as the original expressions derived in Refs. 5 and 6 (see Ref. 9).The Pesch-approximation 7 yields for the spatial average of the normalized density of states:whereHere v ⊥ (k) is the component of the Fermi velocity perpendicular to the magnetic field H , and Σ i (ω) is the self energy for impurity scattering which is calculated self-consistently in the t-matrix approximation. 9 The integrand of the ω-integral for the thermal conductivity is proportional to ω The first term in Eq.[3] is the scattering r...

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“…[3] is the scattering rate due to impurities which reduces in the normal state to Γ = 1/2τ n . The second term is the Andreev scattering rate due to the vortex cores.…”

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Thermal conductivity in the vortex state of the superconductorUPd2Al3

Tewordt

Fay

2005

Phys. Rev. B

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“…As is well known the gap symmetry and the gap function has been the central issue since the discovery of the heavy-fermion superconductors [20]. [25,26], UPd 2 Al 3 [27,28] and CePt 3 Si [29,30] through the angle-dependent thermal conductivity. For a review of these aspects see [31].…”

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Gossamer superconductivity, new paradigm?

Won¹,

Haas

Maki

et al. 2005

Physica Status Solidi (b)

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Key words cuprate, d-wave superconductivity, d-wave density wave PACS 74.70.-b We shall review our recent works on d-wave density wave (dDW) and gossamer superconductivity (i.e. dwave superconductivity in the presence of dDW) in high-Tc cuprates and CeCoIn5. a) We show that both the giant Nernst effect and the angle dependent magnetoresistance (ADMR) in the pseudogap phases of the cuprates and CeCoIn5 are manifestations of dDW. b) The phase diagram of high-Tc cuprates is understood in terms of mean field theory, which includes two order parameters ∆1 and ∆2, where one order paremeter is from dDW and the other from d-wave superconductivity. c) In the optimally to the overdoped region we find the spatially periodic dDW, an analogue of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, becomes more stable. d) In the underdoped region where ∆2/∆1 ≪ 1 the Uemera relation is obtained within the present model. We speculate that the gossamer superconductivity is at the heart of high-Tc cuprate superconductors, the heavy-fermion superconductor CeCoIn5 and the organic superconductors κ-(ET)2Cu(NCS)2 and (TMTSF)2PF6.

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“…Thus the angle dependent magneto-thermal conductivity provides a powerful tool to determine the nodal structure of the gap function as demonstrated by a series of experiments by Izawa et al [5][6][7][8][9][10][11][12]. Also in most cases the nodal structure of the gap function is adequate to deduce |∆(k)| itself.…”

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confidence: 99%