186
J.-P. Brison
These two states have also S = 0 and L = 0; however, the planar state has point
nodes along the z-axis whereas the polar state has a line of nodes on the equator.
Both are also unitary, ESP states (see Sect. 6.5.3).
6.8.2 UPt 3 and Sr 2 RuO 4
UPt 3 is a ‘heavy fermion’ metal, meaning that it is an inter-metallic system with
very strong electronic correlation effects, leading to a strong renormalization of the
effective mass of the electronic quasiparticles. It has been the first heavy fermion
where these effective masses have been directly measured (up to 160 times the free
electron mass) on the different Fermi sheets, by quantum oscillations, and it has also
been the first superconducting system (after superfluid
3 He) where phase transitions
between different superconducting phases have been observed (see [6] for a review
and Fig. 6.4).
6.8.2.1 Phases of UPt 3
The reasons leading to these phase transitions and the nature of the various superconducting phases have been the subject of many different proposals. There is a global
consensus that superconductivity in UPt 3 should be triplet (odd parity). Nevertheless, many questions remain without a definite answer. A first (still open) question,
for example, is whether or not the spin component is free to rotate in the hexagonal
crystal lattice of UPt 3 . This will determine the response of UPt 3 under the application
of an external field when it is superconducting. The orbital part (the k-dependence)
of the superconducting order parameter is constrained by the broken symmetries in
the superconducting state inducing, for example, nodes of the order parameter and so
of the gap in some particular directions: if spin–orbit coupling is strong enough, then
the d-vector is expected to be pinned in some crystal direction; if spin–orbit coupling
is weak, as in superfluid
3 He, the d-vector should be free to rotate and the response
to a magnetic field should have the same anisotropy as in the normal phase. Because
pairing is mainly driven by the 5 f electrons, spin–orbit coupling is expected to be
strong also for the Cooper pair wave function, and pinning of the d-vector is likely.
However, this hypothesis has no definite experimental support (see Sect. 6.8.2.3).
6.8.2.2 E 2u Representation
Among the models assuming such a strong spin–orbit coupling pinning the dvector in a fixed crystallographic direction, the so-called E 2u representation has
been strongly developed. It is an ‘f -wave’ order parameter, which can have various
symmetries (six basis functions are necessary to describe the most general order
parameter). Among these, the most successful [7] proposes a d-vector with some
J.-P. Brison
These two states have also S = 0 and L = 0; however, the planar state has point
nodes along the z-axis whereas the polar state has a line of nodes on the equator.
Both are also unitary, ESP states (see Sect. 6.5.3).
6.8.2 UPt 3 and Sr 2 RuO 4
UPt 3 is a ‘heavy fermion’ metal, meaning that it is an inter-metallic system with
very strong electronic correlation effects, leading to a strong renormalization of the
effective mass of the electronic quasiparticles. It has been the first heavy fermion
where these effective masses have been directly measured (up to 160 times the free
electron mass) on the different Fermi sheets, by quantum oscillations, and it has also
been the first superconducting system (after superfluid
3 He) where phase transitions
between different superconducting phases have been observed (see [6] for a review
and Fig. 6.4).
6.8.2.1 Phases of UPt 3
The reasons leading to these phase transitions and the nature of the various superconducting phases have been the subject of many different proposals. There is a global
consensus that superconductivity in UPt 3 should be triplet (odd parity). Nevertheless, many questions remain without a definite answer. A first (still open) question,
for example, is whether or not the spin component is free to rotate in the hexagonal
crystal lattice of UPt 3 . This will determine the response of UPt 3 under the application
of an external field when it is superconducting. The orbital part (the k-dependence)
of the superconducting order parameter is constrained by the broken symmetries in
the superconducting state inducing, for example, nodes of the order parameter and so
of the gap in some particular directions: if spin–orbit coupling is strong enough, then
the d-vector is expected to be pinned in some crystal direction; if spin–orbit coupling
is weak, as in superfluid
3 He, the d-vector should be free to rotate and the response
to a magnetic field should have the same anisotropy as in the normal phase. Because
pairing is mainly driven by the 5 f electrons, spin–orbit coupling is expected to be
strong also for the Cooper pair wave function, and pinning of the d-vector is likely.
However, this hypothesis has no definite experimental support (see Sect. 6.8.2.3).
6.8.2.2 E 2u Representation
Among the models assuming such a strong spin–orbit coupling pinning the dvector in a fixed crystallographic direction, the so-called E 2u representation has
been strongly developed. It is an ‘f -wave’ order parameter, which can have various
symmetries (six basis functions are necessary to describe the most general order
parameter). Among these, the most successful [7] proposes a d-vector with some