Superfluid transition temperature in a Fermi gas with repulsion allowing for higher orders of perturbation theory

Abstract

High order perturbation theory corrections to the superfluid transition temperature in a weakly interacting Fermi gas with repulsive interaction are calculated. This involves calculating the contributions of third and fourth order diagrams in the gas parameter ap F and taking into account effects of retardation. The contributions from both second, third and fourth orders result in the effective attraction in p-wave channel. It is shown that the critical temperature is mainly determined by second and third orders terms of perturbation theory. The dependence of the critical temperature on an external magnetic field is found. We discuss possible applications of the results to the diluted 3 He-4 He mixtures and trapped neutral-atom Fermi gases.

Weak3He Pairing in3He-He(II) Mixtures

“…The type of pairing which has the higher transition temperature may take place. It has been predicted that dilute 3 He-He(II) mixtures favor s-wave pairing at x < 3% [10,34]. In this range the scattering length corresponds to attraction; so that s-wave pairing may occur.…”

“…On the other hand, the interaction tends to produce p-wave coupling at x > 3%. Therefore the instability of our system exists thanks to the Kohn-Luttinger mechanism at x > 3% [10,35]. The triplet transition temperature T (p) c can be calculated using [12]:…”

“…This involved calculating the contributions of third-and fourth-order diagrams in the gas phase and taking into account retardation effects. Estimates of the superfluid transition temperature for 3 He in 3 He-He(II) range from 10 −5 -10 −4 K for singlet pairing at low x, and 10 −10 -10 −4 K for triplet pairing at higher x [10][11][12][13]. However, no experimental evidence has yet been found for such a transition.…”

“…In addition, by "tuning" the 3 He concentration x, both s-wave and p-wave pairing can presumably be brought into dominance [10,11]. The first calculation of the transition temperature on the basis of an effective interaction in momentum space was achieved by Bardeen et al [6].…”

“…In Ref. [10], the superfluid transition temperatures in 3 He-He(II) mixtures (the 3 He concentration being more than 3%), with a repulsive interaction, were calculated using high-order perturbation theory corrections. This involved calculating the contributions of third-and fourth-order diagrams in the gas phase and taking into account retardation effects.…”