Second sound driven by the combined action of resistive and normal phonon scatterings in nonmetallic materials

The recent observation of second sound in graphite at near room temperature has sparked great interest in studying second sound phenomenon. In this work, a damped vibration equation for temperature field describing second sound co-driven by resistive and normal scatterings is derived from the phonon Boltzmann transport equation with Callaway’s approximation. The thermal conductivity obtained from the damped vibration equation for temperature field shows an agreement with the experimental results for suspended single-layer graphene. It is found that there exists a critical length for heat conduction problems described by the initial-boundary value problem of the damped vibration equation for temperature field, second sound can only emerge when the length of the heat conduction region is smaller than this critical length. Furthermore, an expression for second sound velocity is derived, which shows that the second sound velocity depends on the length of the heat conduction region. These findings will contribute to the experimental study of second sound in low-dimensional nonmetallic materials.