Cooling via Expansion: a Generalized Joule-Thomson Effect for Hydrodynamic Electrons

The Joule-Thomson (JT) effect, arising from isenthalpic expansion of a gas, is a powerful and commonly used refrigeration technique. In everyday life, it is often seen in the cold outflow of a compressed air canister through a constricted nozzle. While cooling occurs for attractive gases, for repulsive fluids like a Fermi gas the JT process typically leads to heating. With the discovery of hydrodynamic electron systems in materials, we revisit the JT effect in these systems and find that it is distinct from its ``free space'' counterparts; the presence of electrochemical potential modifies the nature of expansion. By properly considering the additional contribution of the electrochemical potential to the energy budget, a generalized enthalpy is shown to be conserved during the expansion. We study non-interacting fermionic and bosonic systems of various dispersions and find that they all experience cooling under this generalized JT process. Estimating the size of the JT coefficient for graphene in the Fermi liquid regime, we estimate the temperature drop to be ~ 100 K/eV. Such an effect may be experimentally observable in constriction or nozzle geometries.