  We investigate transport in graphene supported on various dielectrics (SiO2,
BN, Al2O3, HfO2) through a hydrodynamic model which includes self-heating and
thermal coupling to the substrate, scattering with ionized impurities, graphene
phonons and dynamically screened interfacial plasmon-phonon (IPP) modes. We
uncover that while low-field transport is largely determined by impurity
scattering, high-field transport is defined by scattering with
dielectric-induced IPP modes, and a smaller contribution of graphene intrinsic
phonons. We also find that lattice heating can lead to negative differential
drift velocity (with respect to the electric field), which can be controlled by
changing the underlying dielectric thermal properties or thickness. Graphene on
BN exhibits the largest high-field drift velocity, while graphene on HfO2 has
the lowest one due to strong influence of IPP modes.
