Hot carrier relaxation in three dimensional gapped Dirac semi-metals

We calculate the relaxation rate of hot carriers in a Cd3As2 semi-metal with a finite gap. The quantization of the transverse momentum gives rise to a minimum gap at the Dirac point. Additional chemical doping further increases the gap. A finite gap relaxes the selection rule and gives rise to a nonvanishing internode coupling via phonon scattering. The gap also enhances the intra-node scattering. It is shown that the relaxation rate is proportional to the square of the gap. By considering the decay of the electron distribution function, we find that the relaxation rate increases with the square of the gap and the electron temperature.