Anomalous electronic energy relaxation and soft phonons in the Dirac semimetal Cd$_3$As$_2$

We have used a combination of linear response time-domain THz spectroscopy (TDTS) and high-field non-linear THz spectroscopy to separately probe the electronic momentum and energy relaxation rates respectively of the Dirac semimetal Cd$_3$As$_2$. We find, consistent with prior measurements, that Cd$_3$As$_2$ has an enormous nonlinearities in the THz frequency range. We extract the momentum relaxation rate of Cd$_3$As$_2$ using Drude fits to the optical conductivity. We also conduct THz range 2D coherent spectroscopy. The dominant response is a pump-probe signal, which allow us to separately extract the energy relaxation rate. We find that the rate of energy relaxation decreases down to the lowest measured temperatures. We connect this to Cd$_3$As$_2$ anomalous lattice dynamics, evidence for which is found in its low thermal conductivity and soft phonons in Raman scattering. The lack of a peak in the energy relaxation rate as a function of T can be connected to the linear in T dependence of the current relaxation e.g. the phonon scattering is elastic down to the lowest measured temperatures approximately 120 K.