The superconducting phases of ${\mathrm{UPt}}_3$

The heavy-fermion compound ${\mathrm{UPt}}_3$ is the first compelling example of a superconductor with an order parameter of unconventional symmetry. To this day, it is the only unambiguous case of multiple superconducting phases. Twenty years of experiment and theory on the superconductivity of ${\mathrm{UPt}}_3$ are reviewed, with the aim of accounting for the multicomponent phase diagram and identifying the superconducting phases. First, the state above the superconducting critical temperature at $T_c=0.5\mathrm{}\mathrm{K}$ is briefly described: de Haas–van Alphen and other measurements demonstrate that this state is a Fermi liquid, with degeneracy fully achieved at $T_c.$ This implies that the usual BCS theory of superconductivity should hold, although the strong magnetic interactions suggest the possibility of an unconventional superconducting order parameter. The role of the weak antiferromagnetic order below $T_N=5\mathrm{}\mathrm{K}$ in causing phase multiplicity is examined. A comprehensive analysis of which superconducting states are possible is given, and the theoretical basis for each of the main candidates is considered. The behavior of various properties at low temperature $(T\ll T_c)$ is reviewed. The experiments clearly indicate the presence of nodes in the superconducting gap function of all three phases. In particular, the low-temperature low-field phase has a gap with a line node in the basal plane and point nodes along the hexagonal $c$ axis. The phase diagram in the magnetic-field–temperature plane has been determined in detail by ultrasound and thermodynamic measurements. Experiments under pressure indicate a coupling between antiferromagnetism and superconductivity and provide additional clues about the order parameter. Theoretically, Ginzburg-Landau theory is the tool that elucidates the phase diagram, while calculations of the temperature and field dependence of physical quantities have been used to compare different order parameters to experiment. On balance, the data point to a two-component order parameter belonging to either the $E_{1g}$ or the $E_{2u}$ representation, with degeneracy lifted by a coupling to the symmetry-breaking magnetic order. However, no single theoretical scenario is completely consistent with all the data. The coupling of superconductivity and magnetism may be the weakest link in the current picture of ${\mathrm{UPt}}_3,$ and full understanding depends on the resolution of this issue.