Numerical study on the transition from coherent to incoherent phonon transport in a superlattice

Superlattice has been widely investigated due to its capability of modulating phonon dispersion and suppressing transport. However, increases of superlattice periodicity and temperature cause phonon decoherence and then suppress the reduction of lattice thermal conductivity [1], which is well known as the issue for developing heat conduction control by superlattice. Here a criterion for which phonon coherence is preserved needed to be identified. Ref. [2] derived the phonon coherence condition with respect to wavelength and temperature as λ≥(hv/kBT) with speed of sound (v), however, we addressed this issue from different viewpoint, namely, the uncertainty associated with energy and momentum conservations; it should be satisfied that not only the multiplication of phonon frequency ω and relaxation time τ is large enough (ωτ»1) but also fluctuation of momentum δ(hk/2π) is sufficiently smaller than reciprocal lattice vector G(=2π/a) (δ(hk/2π)«hG/2π), where a denotes periodicity. These discussions finally result in the relationship T≤(hvg/kBa), where vg denotes group velocity. By using molecular dynamics simulations, we will report the verification of this formula.
[1] Phys. Rev. Lett. 84, 927 (2000). [2] AIP Advances 6, 065024 (2016).