Ingredients for triplet superconductivity

It is well established that in superfluid 3He that the Cooper pairs are in a spin triplet state. It is believed that this results from ferromagnetic spin fluctuations within the normal Fermi liquid state.

It remains to be established whether there are any superconductors in a spin triplet state. The most promising candidates are Strontium Ruthenate (Sr2RuO4) [see this review by Andy Mackenzie and Yoshi Maeno] and the Bechgaard salts (TMTSF)2X [see this PRB].

I assumed that a necessary ingredient for triplet superconductivity would be Cooper pairing via exchange of ferromagnetic spin fluctuations. However, I learnt this week that this is not the case. It seems that in quasi-one-dimensional quarter-filled bands (as in the Bechgaard salts)  charge fluctuations and the associated competition between CDW and SDW order can lead to an associated competition between spin triplet "f-wave" pairing and spin singlet "d-wave" pairing. The figure below shows that associated signs of the order parameter over the first Brilloiun zone and Fermi surface.

[The figure is taken from a paper by Kuroki and Tanaka]. Note that the variation in the magnitude of the order parameter over different parts of the Fermi surface is the same for both. Just the sign is different on the two Fermi surface sheets. Hence, it is conceivable that a particular pairing interaction should lead to these two states being competitive with one another.

This PRL provides a renormalisation group analysis which illustrates this competition and highlights the importance of reducing the Fermi surface nesting to produce the triplet state. A recent PRL suggests similar considerations may actually also apply to strontium ruthenate.

I thank Nigel Hussey and Jaime Merino for introducing me to the literature.