PAIRING IN FERMI FLUIDS IN RESTRICTED GEOMETRIES

Abstract

We consider dimerization of 3 He in a dilute solution of 3 He in superfluid 4 He filling narrow channels of a kind typically found in nanoscale porous media. Dimer formation is facilitated by the one dimensional geometry and occurs despite the fact that the interparticle interaction is too weak to lead to a bound state in bulk fluid. At sufficiently low temperatures, dimerization results in the effective "bosonization" of the system: a Bose quantum fluid of (3 He )2 arises in place of the 3 He Fermi component. At sufficiently high temperatures, for which the 3 He impurity quasiparticles form a Maxwell–Boltzmann gas, the thermodynamics is significantly affected by the presence of dimers. In particular, the specific heat and magnetic susceptibility of the 3 He component show a marked deviation from behaviour expected if dimers were absent. Solution of the Schrödinger equation for a smooth cylindrical pore indicates that the binding energy in straight nanoscale channels ought to be of sufficiently high magnitude to make experimental observation feasible. The presence of (3 He )2 dimers gives rise to an extra absorption mechanism for first sound propagating through the superfluid 4 He , due to resonant absorption and decay of dimers in the acoustic field. We have calculated the absorption coefficient. Several experiments suggest themselves, utilizing, perhaps, K-L zeolites or carbon nanotubes. If the dimers themselves turn out to be attractive, then quadrumers may appear: it may even be the case that a single 3 He polymer will form over the entire length of the channel.