Strong-coupling theory of superfluid transition temperatures for paramagnon models: Application to He3

The triplet superconducting transition temperature Tc for l=1 paramagnon-induced pairing is computed within a Matsubara formulation of conventional strong-coupling theory, as a function of the interaction parameter Ī. Using the scattering amplitudes of Fermi-liquid theory to fix Ī for He3 at each pressure, we apply our results to He3. The computed values of Tc differ by less than a factor of 5 from those measured experimentally but the (slight) pressure dependence and the effective mass ratio Z=m*m are incorrect. If Z is adjusted to be in better accord with experiment, we then obtain reasonable agreement with the measured magnitude and pressure dependence of Tc over the entire pressure range. General features of the paramagnon model are (i) Tc(Ī) has a maximum value of 10-2∼10-3 of the Fermi temperature TF at Ī0.995; it seems doubtful that even under the most ideal conditions the paramagnon mechanism can be used to obtain high-temperature superconductors; (ii) Tc(Ī) vanishes by Ī=1. (iii) Below Ī∼0.97, the exponential form Tc=ω̄ce-bλ is obtained where b is close to unity, ω̄c is a constant of order TF10, and λ is the renormalized coupling constant λΔZ. The previously proposed analogous expression involving the spin-fluctuation frequency ωsf, Tc=ωsfe-1λ, is inconsistent with our results over the entire range of Ī. Strong-coupling corrections, deriving from the mass ratio Z, are extremely important in He3: They reduce the size of Tc by nearly two orders of magnitude and help make it relatively pressure insensitive. While the paramagnon model is undoubtedly an oversimplified description of He3, a strong-coupling calculation within this model represents a significant improvement over previous approaches in which theoretical values of Tc have differed from experiment by orders of magnitude or in which either ωc or λ have been chosen to fit the Tc data.