## CMT 60

##
The Order Parameter for the Superconducting Phases of UPt_{3}

**Author(s):** J. A. Sauls

**Comments:** 33 pages with 4 figures in Postscript

**Journal:** Adv. Phys. 43, 113 (1994)
[DOI]
**Abstract:**

I review the principal
theories that have been proposed for the superconducting phases of UPt_{3}.
The detailed H-T phase diagram places constraints on any theory for the
multiplesupercond cting phases. Much attention has been given to the Ginzburg-Landau
(GL) region of the phase diagram where the phase boundaries of three phases
appear to meet at a tetracritical point. I has been argued that the existence
of a tetracritical point for all field orientations eliminates the two-dimensional
(2D) orbital representations coupled to a symmetry breaking field (SBF)
as viable theory of these phases, and favors either (i) a theory
based on two primary order parameters belonging to different irreducible
representations that are accidentally degenerate [Chen and Garg, Phys.
Rev. Lett. 70, 1689 (1993)], or (ii) a spin-triplet, orbital one-dimensional
(1D) representation with no spin-orbit coupling in the pairing channel
[Machida and Ozaki, Phys. Rev. Lett. 66, 3293 (1991)]. I comment on the
limitations of the models proposed so far for the superconducting phases
of UPt_{3}. I also find that a theory in which the order parameter
belongs to an orbital 2D representation coupled to a SBF is a viable model
for the phases of UPt_{3}, based on the existing body of experimental
data. Specifically, I show that (1) the existing phase diagram (including
an apparent tetracritical point for all field orientations), (2) the anisotropy
of the upper critical field over the full temperature range, (3) the correlation
between superconductivity and basal plane antiferromagnetism and (4) low-temperature
power laws in the transport and thermodynamic properties can be explained
qualitatively, and in many respects quantitatively, by an odd-parity, E_{2u}
order parameter with a pair spin projection of zero along the c-axis. The
coupling of an AFM moment to the superconducting order parameter acts as
a symmetry breaking field (SBF) which is responsible for the apparent tetracritical
point, in addition to the zero-field double transition. The new results
presented here for the E_{2u} representation are based on
an analysis of the material parameters calculated within BCS theory for
the 2D representations, and a refinement of the SBF model of Hess, et al.
[J. Phys. Condens. Matter, 1, 8135 (1989)]. I also discuss possible
experiments to test the symmetry of the order parameter.

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