What can superconductivity learn from quantized vorticity in 3 He superfluids ?

In 3 He superfluids quantized vorticity can take many different forms: It can appear as distributed periodic textures, as sheets, or as lines. In the anisotropic 3 He-A phase in most cases the amplitude of the order parameter remains constant throughout the vortex structure and only its orientation changes in space. In the quasi-isotropic 3 He-B phase vortex lines have a hard core where the order parameter has reduced, but finite amplitude. The different structures have been firmly identified , based on both measurement and calculation. What parallels can be drawn from this information to the new unconventional superconductors or Bose-Einstein condensates? 1 Unconventional quantized vorticity Soon after the discovery of the 3 He superfluids in 1972 it was understood that they represented the first example of unconventional Cooper pairing among Fermi systems, a p-wave state with total spin S = 1 and orbital momentum L = 1 [1]. This lead to a wide variety of new phenomena, of which one of the most important is the discovery of new vortex structures [2]. These can be studied with NMR spectroscopy [3], when this is combined with a calculation of the order parameter texture [4]. In recent years other unconventional macroscopic quantum systems have been found and have taken the centre stage. Intermetallic alloys such as the heavy fermion metals, the high-temperature superconductors, and the most recent addition, the layered superconductors of Sr 2 RuO 4 type, do not fit in the conventional picture of s-wave pairing. Is it possible that unconventional vortex structures, similar perhaps to some of those in the 3 He superfluids, might also be present in these new systems? Current belief holds that the superconducting state in the tetragonal Sr 2 RuO 4 material is described by an order parameter of the same symmetry class as that in 3 He-A [5,6], an anisotropic superfluid with uniaxial symmetry (where both time reversal symmetry and reflection symmetry are spontaneously broken). Recent advances in optical trapping and cooling of alkali atom clouds to Bose-Einstein condensates have produced Bose systems which also are described by a multi-component order parameter: The spinor