  Superlattices provide a great platform for studying coherent transportation
of low-frequency phonons, which are the main issues in mastering the
manipulation of heat conduction. Studies have shown that the dominating
characteristics in the thermal conductivity of superlattice can be adjusted
between wave-like and particle-like phonon properties depending on the
superlattice period. However, the phonon coherence length and the phonon mean
free path from Umklapp processes have not been defined in one superlattice
system, and the transition from wave-like and particle-like behavior is not
clear to date despite the extensive research efforts. In this study, we use
InGaO3(ZnO)m (m = integer) single crystal films with superlattice structure to
experimentally characterize the phonon coherence length as well as the Umklapp
mean free path in one system. According to the results, the nature of heat
conduction in superlattice can change in three different ways depending on the
ratio between the phonon coherence length and the superlattice period. We also
discuss the role of the phonon characteristic lengths in the heat conduction of
superlattices and its anisotropy.
