The order parameter for the superconducting phases of UPt3

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Abstract
I review the principal theories that have been proposed for the superconducting phases of UPt3. The detailed H-T phase diagram places constraints on any theory for the multiple superconducting phases. Much attention has been given to the Ginzberg-Landau region of the phase diagram where the phase boundaries of three phases appear to meet at a tetracritical point. It 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 a viable theory of these phases and favours either a theory based on two primary order parameters belonging to different irreducible representations that are accidentally degenerate, as described by Chen and Garg 1993, or a spin-triplet, orbital one-dimensional representation with non spin-orbit coupling in the pairing channel, as described by Machida and Ozaki 1991. I comment on the limitations of the models proposed so far for the superconducting phases of UPt3. 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 UPt3, based on the existing body of experimental data. Specifically, I show that the existing phase diagram (including an apparent tetracritical point for all field orientations), the anisotropy of the upper critical field over the full temperature range, the correlation between superconductivity and basal plane antiferromagnetism and the low-temperature power laws in the transport and thermodynamic properties can be explained qualitatively, and in many respects quantitatively, by an odd-parity E2u order parameter with a pair spin projection of zero along the ˆc axis. The coupling of an antiferromagnetic moment to the superconducting order parameter acts as a SBF which is responsible for the apparent tetracritical point, in addition to the zero-field double transition. The new results presented here for the E2u representation are based on an analysis of the material parameters calculated within the Bardeen-Cooper-Schrieffer theory for the 2D representations, and a refinement of the SBF model given by Hess et al. (1989). I also discuss possible experiments to test the symmetry of the order parameter.
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