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.