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The compositional as well as structural asymmetries in Janus transition metaldichalcogenides (J-TMDs) and their van der Waals heterostructures (vdW HSs)induce an intrinsic Rashba spin-splitting. We investigate the variation ofband-gaps and the Rashba parameter in three different Janus heterostructureshaving AB-stacked Mo$XY$/W$XY$ ($X$, $Y$ = S, Se, Te; $X\neq Y$) geometry witha $Y-Y$ interface, using first-principles calculations. We consider the effectof external electric field and in-plane biaxial strain in tuning the strengthof the intrinsic electric field, which leads to remarkable modifications of theband-gap and the Rashba spin-splitting. In particular, it is found that thepositive applied field and compressive in-plane biaxial strain can lead to anotable increase in the Rashba spin-splitting of the valence bands about the$\Gamma$-point. Moreover, our \textit{ab-initio} density functional theory(DFT) calculations reveal the existence of a type-II band alignment in theseheterostructures, which remains robust under positive external field andbiaxial strain. These suggest novel ways of engineering the electronic,optical, and spin properties of J-TMD van der Waals heterostructures holding ahuge promise in spintronic and optoelectronic devices. Detailed $\mathbf{k\cdotp}$ model analyses have been performed to investigate the electronic and spinproperties near the $\Gamma$ and K points of the Brillouin zone.

Electric field and Strain-induced Band-gap Engineering and Manipulation of the Rashba Spin Splitting in Janus van der Waals Heterostructures