Superfluid Fermi systems

Abstract

A system of particles with pair interaction can possess microscopic coherent properties both in the Bose- and Fermi-statistics cases. For Fermi particles, such properties are related to their ability to combine in pairs which show up as new Bose particles. For individual Fermi particles, the ordering of the type of Bose condensate is impossible because of the Pauli principle; however, the exclusion principle does not extend to paired fermions. The best known example is the superconductivity of certain metals at low temperatures. This phenomenon is based on the fact that for the free electrons in a metal, separation into pairs with singlet total spin value (that is, equal to zero) and with zero total momentum turns out to be energetically advantageous at sufficiently low temperatures [2]. Such electron pairs (so-called Cooper pairs) preserve their total momentum on interaction with the lattice, leading to a virtually unimpeded movement in the metal.¹ This effect can be regarded as a condensation of pairs, while the phenomenon of superconductivity can be regarded as a special kind of superfluidity in a Fermi gas. It turns out that fermions can also combine in pairs at a non-zero total spin value (p-state). Such a phenomenon occurs in liquid ³He the nuclei of the atoms of which are fermions, since they contain only one neutron in contrast to the kernels of ⁴He atoms.