A theory for the superconducting phases of UPt₃

I discuss a phenomenological theory for the multiple superconducting phases of UPt₃ that is based on an order parameter belonging to an orbital 2D representation of the hexagonal point group which is coupled to a weak symmetry breaking field. I show that (1) the existing H-T and P-T phase diagrams (including an apparent tetracritical point in the H-T plane 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 ĉ-axis. AFM ordering in the basal plane, which couples to the superconducting order parameter, acts as the symmetry breaking field that is responsible for both the apparent tetracritical point and the zero-field double transition.