  For a system of two spatially separated monoatomic graphene layers
encapsulated in hexagonal boron nitride, we consider the drag effect between
charge carriers in the Fermi liquid regime. Commonly, the phenomenon is
described in terms of an interlayer Coulomb interaction. We show that if an
additional electron - electron interaction via exchange of virtual substrate
phonons is included in the model, the predicted drag resistivity is modified
considerably at temperatures above 150 K. The anisotropic crystal structure of
boron nitride, with strong intralayer and comparatively weak interlayer bonds,
is found to play an important role in this effect.
