E1gmodel of superconductingUPt3

Abstract

The phase diagram of superconducting UPt 3 is explained in a GinzburgLandau theory starting from the hypothesis that the order parameter is a pseudo-spin singlet which transforms according to the E 1g representation of the D 6h point group. We show how to compute the positions of the phase boundaries both when the applied field is in the basal plane and when it is along the c-axis. The experimental phase diagrams as determined by longitudinal sound velocity data can be fit using a single set of parameters. In particular the crossing of the upper critical field curves for the two field directions and the apparent isotropy of the phase diagram are reproduced. The former is a result of the magnetic properties of UPt 3 and their contribution to the free energy in the superconducting state. The latter is a consequence of an approximate particle-hole symmetry. Finally we extend the theory to finite pressure and show that, in contrast to other models, the E 1g model explains the observed pressure dependence of the phase boundaries.

Transport and the order parameter of superconductingUPt3

“…In the B phase with g (2) = 0 there are lines of nodes along the equator and point nodes at the poles. Changing the ratio of g (1) and g (2) does not affect this nodal pattern. A larger value of g (2) merely gives additional modulation to the order parameter in the azimuthal direction.…”

“…There is very little change in the goodness of fit as the ratio is varied. Defining a chisquare parameter for the fits as a function of g (2) /g (1) , we see from its approximate constancy that the E 1g theory is robust for this particular quantity.…”

“…There are only two parameters g (1) and g (2) . In the B phase with g (2) = 0 there are lines of nodes along the equator and point nodes at the poles.…”

“…The main difference between E 2u and E 1g is clear from the nodal pattern. Taking into account u (1) in addition to the usual u (2) , when u (1) = 0 there is a line of nodes at the equator and point nodes at the poles in the B phase. When u (1) is finite, however, the line of nodes disappears.…”

“…This includes the E 1g [1] and E 2u [2] theories. Because of the perception that these theories may not give sufficient phenomenological flexibility, other pictures have been constructed.…”