  Being used in optoelectronic devices as ultra-thin conductor-insulator
junctions, detailed investigations are needed about how exactly h-BN and
graphene hybridize. Here, we present a comprehensive ab initio study of hot
carrier dynamics governed by electron-phonon scattering at the h-BN/graphene
interface, using graphite (bulk), monolayer and bilayer graphene as benchmark
materials. In contrast to monolayer graphene, all multilayer structures possess
low-energy optical phonon modes that facilitate carrier thermalization. We find
that the h-BN/graphene interface represents an exception with comparatively
weak coupling between low-energy optical phonons and electrons. As a
consequence, the thermalization bottleneck effect, known from graphene,
survives hybridization with h-BN but is substantially reduced in all other
bilayer and multilayer cases considered. In addition, we show that the quantum
confinement in bilayer graphene does not have a significant influence on the
thermalization time compared to graphite and that bilayer graphene can hence
serve as a minimal model for the bulk counterpart.
