  We study plasmon modes of the two-dimensional electron gas residing at the
interface of band insulators $\rm{LaAlO_3}$ and $\rm{SrTiO_3}$ (LAO/STO) and
the plasmon excitations of graphene-LAO/STO double layer as well. Considering
the electron-electron interaction within random phase approximation, we
calculate the plasmon dispersions of both systems numerically and in the long
wavelength limit analytical expressions for collective modes are found. One
optical mode and two (three) acoustic modes are predicted for the LAO/STO
(graphene-LAO/STO) system where only the uppermost acoustic mode of both
systems can emerge above the electron-hole continuum depending on the
characteristics of each system. In the case of LAO/STO interface, thanks to the
spatial separation between $\rm{t_{2g}}$ orbitals, the upper acoustic mode
might be undamped at the long wavelength limit depending on the exact value of
the dielectric constant of $\rm{SrTiO_3}$. Same as other double layer systems,
the interlayer distance for the graphene-LAO/STO system plays a crucial role in
damping the upper acoustic mode. Faster damping of all plasmon modes of the
present double layer system in comparison with the ones with conventional 2DEG
instead of $\rm{t_{2g}}$ electron gas is also found due to heavier effective
masses of the gas and also stronger interlayer Coulomb interaction.
