Nonzero mean value of phonon angular momentum (PAM) in chiral materials can be generated when a temperature gradient is applied. We find that both diagonal and off-diagonal terms of PAM contribute to mean PAM by using the Kubo formula where both diagonal and off-diagonal elements of the heat current operator are considered. The calculation results show that the off-diagonal term is dominant when the phonon scattering is strong enough. This finding reveals that the quantum transition between different phonon modes induced by temperature gradient strongly affects the local atomic rotation. Our discovery provides an explanation of the recently observed chiral phonon activated spin Seebeck effect.
