Two Distinct Phonon Wave Effects Control Thermal Transport across the Coherent-Incoherent Regime in Superlattices

Superlattices composed of nanometer-thick constituent layers with smooth interfaces exhibit a minimum in their cross-plane thermal conductivity as the period thickness is increased, marking a transition from coherent to incoherent phonon transport. Previous attempts to explain this minimum using the phonon Boltzmann transport equation (BTE) required an ad hoc diffuse interface scattering model due to the BTE's inherent particle-based framework. We apply the phonon Wigner transport equation (WTE) to study superlattices with smooth interfaces, a framework that inherently includes both the particle-like (i.e., population-channel) and wave-like (i.e., coherence-channel) contributions to thermal conductivity. Our results reveal that the WTE coherence channel is responsible for the thermal conductivity increase in the incoherent regime. The two distinct phonon wave effects in superlattices-the coherent transport induced by wave interference at the interfaces and the WTE coherence-channel transport enabled by tunneling between phonon modes-are examined in detail, along with their connection to the interfacial vibrational modes.