  Placing and twisting graphene on transition metal dichalcogenides (TMDC)
forms a van der Waals (vdW) heterostructure. The occurrence of Zeeman splitting
and Rashba spin-orbit coupling (SOC) changes graphene's linear dispersion and
conductivity. Hence, this paper studies the dependence of graphene's
longitudinal optical conductivity on Rashba SOC, the twist-angle and
temperature. At zero temperature, a main conductivity peak exists. When Rashba
SOC increases, a second peak occurs, with both extremes presenting an enhanced
height and width, and the frequencies where the two peaks arise will increase
because the energy gap and the possibility of electron transition increase.
Altering the twist-angle from 0 to 30$^{\circ}$, the conductivity is primarily
affected by chalcogen atoms. Moreover, when temperature increases to room
temperature, besides a Drude peak due to the thermal excitation, a new band
arises in the conductivity owing to the joint effect of the thermal transition
and the photon transition.
