Frequency-dependent anharmonic scattering rate assignment in VED with non-additive phonon content

Develop a physically consistent, frequency-dependent anharmonic scattering rate τ_ANH^{-1}(ω) for hexagonal boron nitride phonons within the Van der Waals electrodynamics (VED) framework such that the correct anharmonic decay is attributed to each phonon mode despite the non-additivity of the phonon content function F(q, ω), rather than enforcing only the integrated sum rule over the total anharmonic scattering rate.

Background

Within the VED framework used to model electron–phonon scattering in BN-encapsulated graphene, the authors introduce a phenomenological treatment of anharmonic phonon decay that enforces an integrated sum rule over all modes and layers. However, the phonon content function F(q, ω), which distributes the weight of remote electrodynamic modes, is not additive with respect to individual phonon excitations.

Because F(q, ω) is non-additive, assigning a frequency-dependent anharmonic scattering rate that correctly captures the decay of each distinct phonon mode is not straightforward. The authors therefore resort to a constant anharmonic rate consistent only with the total integrated anharmonic scattering, and explicitly point out that resolving a frequency-resolved τ_ANH{-1}(ω) compatible with F(q, ω) remains unresolved.

References

Consequently, the attribution of a frequency dependent $\tau{-1}_{\rm ANH}(\omega)$ that associates the correct anharmonic decay to each phonon is not possible, and the only constraint that we can satisfy is the sum rule over the total anharmonic scattering rate. We leave the solution of this problem for future investigations.

— Electronic transport in BN-encasulated graphene limited by remote phonon scattering  (2604.00678 - Dinar et al., 1 Apr 2026) in Section 3 (VED results), Computation subsection, after Eq. (2)