The role of the coherent interference of phonons on thermal transport in artificial materials such as superlattices is of intense interest. Recent experimental studies report a non-monotonic trend in thermal conductivity with interface density which is attributed to band-folding of thermal phonons. Various models have been proposed to interpret these measurements, but most make simplifying assumptions that make definitively attributing the trends to the coherent transport difficult. Here, we investigate thermal transport in superlattices in the incoherent limit using the Boltzmann equation with intrinsic phonon dispersions and lifetimes calculated from first-principles. We find that the Boltzmann equation is unable to predict the non-monotonic behavior of thermal conductivity versus superlattice period, supporting the interpretation of phonon interference in recent experiments.

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