  We show that the plasmon spectrum of an ordinary two-dimensional electron gas
(2DEG) hosted in a GaAs heterostructure is significantly modified when a
graphene sheet is placed on the surface of the semiconductor in close proximity
to the 2DEG. Long-range Coulomb interactions between massive electrons and
massless Dirac fermions lead to a new set of optical and acoustic intra-subband
plasmons. Here we compute the dispersion of these coupled modes within the
Random Phase Approximation, providing analytical expressions in the
long-wavelength limit that shed light on their dependence on the Dirac velocity
and Dirac-fermion density. We also evaluate the resistivity in a Coulomb-drag
transport setup. These Dirac/Schroedinger hybrid electron systems are
experimentally feasible and open new research opportunities for fundamental
studies of electron-electron interaction effects in two spatial dimensions.
