Electronic cooling in Weyl and Dirac semimetals

Energy transfer from electrons to phonons is an important consideration in any Weyl- or Dirac-semimetal-based application. In this work, we analytically calculate the cooling power of acoustic phonons, i.e., the energy relaxation rate of electrons which are interacting with acoustic phonons, for Weyl and Dirac semimetals in a variety of different situations. For cold Weyl or Dirac semimetals with the Fermi energy at the nodal points, we find that the electronic temperature $T_e$ decays in time as a power law. In the heavily doped regime, $T_e$ decays linearly in time far from equilibrium. In a heavily doped system with short-range disorder we predict that the cooling power of acoustic phonons is drastically increased because of an enhanced energy transfer between electrons and phonons. When an external magnetic field is applied to an undoped system, the cooling power is linear in magnetic field strength and $T_e$ has square-root decay in time, independent of magnetic-field strength over a range of values.