Helium-3 as a Fermi Liquid
Liquid helium-3 is a textbook Fermi liquid: its atoms are fermions whose collective behavior is described by quasiparticles with an enhanced effective mass.
Fermions in a liquid
A helium-3 atom has an odd number of nucleons and one unpaired nuclear spin, making the atom a fermion. Liquid helium-3 is therefore a dense collection of interacting fermions, and at low temperature it behaves according to Landau's theory of Fermi liquids, one of the foundational frameworks of condensed-matter physics.
Quasiparticles and effective mass
In a Fermi liquid the strongly interacting particles are described as weakly interacting quasiparticles: each real particle dressed by the disturbance it creates in its neighbors. The quasiparticles obey Fermi-Dirac statistics and fill states up to a Fermi surface. Interactions renormalize their properties, so a helium-3 quasiparticle has an effective mass several times the bare atomic mass, and quantities like heat capacity and compressibility follow Fermi-liquid predictions with this enhanced mass.
Consequences for cryogenics
This physics matters directly for dilution refrigeration. In the dilute phase of a helium-3 / helium-4 mixture, the helium-3 behaves as a dilute Fermi gas of quasiparticles moving through the superfluid background. Its heat capacity and enthalpy, which set the cooling power of the mixing chamber, follow from this Fermi-liquid description. The finite solubility and the enthalpy difference across the phase boundary are both consequences of helium-3 being a Fermi system.
Superfluid helium-3
At far lower temperatures, around two millikelvin, liquid helium-3 itself becomes superfluid, but by a different mechanism than helium-4. The fermionic atoms form pairs, analogous to Cooper pairs in a superconductor but with the pairs carrying spin and orbital angular momentum, producing a rich set of superfluid phases. This is well below the operating range of a dilution refrigerator but is a landmark result in the physics of the isotope.
- Helium-3 atoms are fermions with unpaired nuclear spin
- Landau Fermi-liquid theory describes the liquid
- Quasiparticles carry an enhanced effective mass
- Dilute helium-3 as a Fermi gas sets mixing-chamber cooling