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Energy relaxation dynamics in a nodal-line semimetal

We study the temperature relaxation dynamics of nodal-line semimetals after a sudden excitation in the presence of acoustic and optical phonon modes. We find that the nodal line constrains the electron momenta in scattering processes and, as a result, the temperature relaxation due to acoustic phonons is exponential as a function of time. However, depending on initial conditions, other functional forms are possible. In typical pump-probe experiments, the temperature relaxation is linear due to acoustic phonons with rates that vary as $\sim n^{1/2}$ with density. The temperature relaxation due to optical phonons is also linear with rates $\sim n^{-1/2}$ or $\sim n$.