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

The compositional as well as structural asymmetries in Janus transition metal dichalcogenides (J-TMDs) and their van der Waals heterostructures (vdW HSs) induce an intrinsic Rashba spin-splitting. We investigate the variation of band-gaps and the Rashba parameter in three different Janus heterostructures having AB-stacked Mo$XY$/W$XY$ ($X$, $Y$ = S, Se, Te; $X\neq Y$) geometry with a $Y-Y$ interface, using first-principles calculations. We consider the effect of external electric field and in-plane biaxial strain in tuning the strength of the intrinsic electric field, which leads to remarkable modifications of the band-gap and the Rashba spin-splitting. In particular, it is found that the positive applied field and compressive in-plane biaxial strain can lead to a notable 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 these heterostructures, which remains robust under positive external field and biaxial strain. These suggest novel ways of engineering the electronic, optical, and spin properties of J-TMD van der Waals heterostructures holding a huge promise in spintronic and optoelectronic devices. Detailed $\mathbf{k\cdot p}$ model analyses have been performed to investigate the electronic and spin properties near the $\Gamma$ and K points of the Brillouin zone.