Revisiting the question of second sound in germanium

Recent experimental work, when combined with a macroscopic hyperbolic heat equation, claimed the observation of a type of second sound in germanium. However, a complete microscopic picture that captures the mechanism responsible for occurrence of second sound remains elusive. By directly solving the linearized phonon Boltzmann transport equation (LBTE), we take a step in addressing this missing piece. First, by performing an eigendecomposition of the full scattering matrix, we show that the conditions for driftless second sound are not satisfied. Second, by the application of Guyer’s criteria and inspection of the phonon-phonon scattering rates, we show that the conditions for drifting second sound are not satisfied. Furthermore, direct solutions to the LBTE for a frequency modulated heat source do not reveal the presence of an ‘other type’ of second sound. Finally, numerical solutions to the BTE under the relaxation time approximation (RTA) in the 1D frequency-domain thermoreflectance (1D-FDTR) experimental geometry demonstrate that phase lag alone is not a suitable experimental observable for inferring second sound. We conclude by discussing our own ongoing experimental work on germanium using pump-probe spectroscopy.