  The spin and valley polarizations and plasmonics in Van der Waals
heterostructures of strained graphene monolayer on 2D transition metal
dichalcogenide (GrTMD) substrate are reported in this communication. The
substrate induced interactions (SII) involve sub-lattice-resolved, and enhanced
intrinsic spin-orbit couplings, the extrinsic Rashba spin-orbit coupling
(RSOC), and the orbital gap related to the transfer of the electronic charge
from graphene to the substrate. Furthermore, magnetic impurity atoms are
deposited to the graphene surface and the corresponding exchange field is
included in the band dispersion. A Rashba coupling dependent pseudo Zeeman term
arising due to the interplay of SIIs was found to be responsible for the spin
degeneracy lifting and the spin polarization. The latter turns out to be
electrostatic doping and the exchange field tunable and inversely proportional
to the square root of the carrier concentration. The strain field, on the other
hand, brings about the valley polarization. The intra-band plasmon dispersion
for the finite doping and the long wavelength limit has also been obtained. The
dispersion involves the q2/3 behavior and not the well known q1/2 behavior. The
uniform, uniaxial strain does not bring about any change in this behavior.
However, the plasmon dispersion gets steeper for the wavevector perpendicular
to the direction of strain and is flattened for wave vectors along the
direction of the strain with the term responsible for the flattening
proportional to the strain field. The stronger confinement capability of GrTMD
Plasmon compared to that of standalone, doped graphene is an important outcome
of the present work. One finds that whereas the intra-band absorbance of GrTMD
is decreasing function of the frequency at a given strain field, it is an
increasing function of the strain field at a given frequency.
