Statistical Mechanics of Superconductivity pp 189-200 | Cite as

*P*-Wave Superfluidity

Chapter

## Abstract

Superfluidity in liquid

^{3}He was discovered at ultra-low temperatures below around 3 mK by Osheroff, Richardson, and Lee in 1972 (Osheroff et al., Phys Rev Lett 28:885, 1972; Phys Rev Lett 29:920, 1972). The^{3}He atom is composed of two protons, one neutron, and two electrons, each of which carries a spin of magnitude 1∕2, and hence is classified as a fermion according to the spin-statistics theorem. Quantum effects in liquid^{3}He is expected to emerge below*T*_{Q}∼ 3 K according to Table 4.1, and the superfluid transition occurs at about 10^{−3}*T*_{Q}to be attributed to the Cooper-pair condensation. As the atom can be regarded roughly as a rigid sphere, it is clearly impossible for a pair of^{3}He atoms to make up an*s*-wave bound state that has a high probability of occupying the same position in space. However, they may form a bound state while being separated through a higher (*ℓ*≥ 1) channel of expansion ( 8.83) to overcome repulsion. Among various theoretical predictions, superfluidity was soon identified to be associated with*p*-wave (*ℓ*= 1) pairing with total spin*s*= 1. Hence, the bound state has a total of \((2\ell + 1)(2s + 1) = 9\) internal degrees of freedom, which brings unique features to the*p*-wave superfluidity including two distinct phases A and B observed in the bulk (see Fig. 13.1). Here, we survey the fundamentals of this superfluidity (Leggett, Rev Mod Phys 47:331, 1975; Vollhardt and Wölfle, The superfluid phases of helium 3. Taylor & Francis, London, 1990, p 31).## Keywords

Fermi Surface Superfluid Phase Effective Pairing Interaction Quasiparticle Density Anisotropic Fermi Surface
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