THE SUPERFLUID PHASES OF LIQUID 3He: BCS THEORY

Following the success of the original BCS theory as applied to superconductivity in metals, it was suggested that the phenomenon of Cooper pairing might also occur in liquid 3- He , though unlike the metallic case the pairs would most likely form in an anisotropic state, and would then lead in this neutral system to superfluidity. However, what had not been anticipated was the richness of the phenomena which would be revealed by the experiments of 1972. In the first place, even in a zero magnetic field there is not one but two superfluid phases, and the explanation of this involves ideas concerning "spin fluctuation feedback" which have no obvious analog in metals. Secondly, the anisotropic nature of the pair wave function, which in the case of the B phase is quite subtle, and the fact that the orientation must be the same for all the pairs, leads to a number of qualitatively new effects, in particular to a spectacular amplification of ultra-weak interactions seen most dramatically in the NMR behavior. In this chapter I review the application of BCS theory to superfluid 3- He with emphasis on these novel features.

NUCLEAR MAGNETIC RESONANCE AND THE BCS THEORY

The author describes the inspiration for the experiment by Hebel and Slichter to measure the nuclear spin–lattice relaxation time in superconductors, the design considerations for the experiment, the surprising experimental results, their theoretical treatment using the Bardeen–Cooper–Schrieffer theory, and how comparing the nuclear relaxation results with those for ultrasound absorption confirmed the central idea of the BCS theory, the BCS pair wave function.

MIXING OF SINGLET AND TRIPLET PAIRING FOR SURFACE SUPERCONDUCTIVITY

We consider structure of the Cooper wave function for superconductivity in a surface layer. Broken space inversion at the surface results in lifted spin degeneracy and in two branches of the gapped energy spectrum as caused by the spin-orbit interaction. The pair wave function consists of a mixture of both singlet and triplet components. Anisotropy of the Knight shift measurable in the NMR experiments is calculated in the whole temperature regime. Implications for a few known experimental situations is briefly discussed.

THERMODYNAMICS OF SUPERCONDUCTING LATTICE FERMIONS

We consider the Cooper-problem on a lattice model including onsite and near-neighbor interactions. Expanding the interaction in basis functions for the irreducible representations of the point group C4v yields a classification of the symmetry of the Cooper-pair wave function, which we calculate in real-space. A change of symmetry upon doping, from s-wave at low filling fractions, to dx2-y2 at higher filling fractions, is found. Fermi-surface details are thus important for the symmetry of the superconducting wave function. Symmetry forbids mixing of s-wave and d-wave symmetry in the Cooper-pair wave function on a square lattice, unless accidental degeneracies occur. This conclusion also holds for the selfconsistent treatment of the many-body problem, at the critical temperature T c . Below T c , we find temperatures which are not critical points, where new superconducting channels open up in the order parameter due to bifurcations in the solutions of the nonlinear gap-equation. We calculate the free energy, entropy, coherence length, critical magnetic fields and Ginzburg–Landau parameter κ. The model is of the extreme type-II variety. At the temperatures where subdominant channels condense, we find cusps in the internal energy and entropy, as well as BCS-like discontinuities in the specific heat. The specific heat anomalies are however weaker than at the true superconducting critical point and argued to be of a different nature.