Large tunable Rashba spin splitting and piezoelectric response in Janus chromium dichalcogenide monolayers

A mirror asymmetric Janus structure induces Rashba spin splitting (RSS) and a piezoelectric response. Inspired by the recently synthesized layered material CrSSe [Yang, Shi, Wang, Yue, Zheng, Zhang, Gu, Yang, Shadike, Li, and Fu, J. Mater. Chem. A 8, 25739 (2020)], we use first-principles calculations to systematically study the Rashba effect and piezoelectricity of Janus chromium dichalcogenide monolayers $\mathrm{Cr}XY$ ($X\ensuremath{\ne}Y=\text{S,}\phantom{\rule{4.pt}{0ex}}\text{Se,}\phantom{\rule{4.pt}{0ex}}\text{Te}$), as well as their regulation with biaxial strain. Our results reveal that spin-orbit coupling (SOC) plays an important role in the electronic properties (such as the semiconductor type, RSS, and valley polarization) of a $\mathrm{Cr}XY$ monolayer. Due to the mirror symmetry break and strong SOC, the strain-free $\mathrm{Cr}XY$ exhibits large Rashba parameters. Specifically, the Rashba parameter of CrSeTe is as high as 1.23 eV \AA{}. Due to the ${\mathit{k}}^{3}$ term in the valence-band edge, the CrSeTe exhibits a strong hexagonal warping effect along with a nonzero out-of-plane spin polarization ${\mathit{S}}_{z}$, which can also be found in the CrSSe and CrSTe monolayers in the lower energy valence bands. Moreover, the Janus $\mathrm{Cr}XY$ monolayer exhibits superior intrinsic piezoelectric responses (${\mathit{d}}_{31}$ = $0.4--0.83$ pm/V), which are orders of magnitude larger than those of the $\mathrm{Mo}XY$ monolayer. Furthermore, we reveal in detail the modulation of the band structure, RSS, and piezoelectric properties with biaxial strain. Tensile strain suppresses the band gap, whereas compressive strain increases the band gap. Thus, strain engineering can effectively tune the band structures resulting in semiconductor-metal and indirect-direct transitions. In addition, the strain has opposite effects on the RSS and the piezoelectricity; that is, unlike compressive strain-enhanced RSS, the tensile strain can significantly elevate the piezoelectric coefficients. Our results indicate that a Janus $\mathrm{Cr}XY$ monolayer has coexisting large intrinsic RSS and piezoelectricity, which can be efficiently regulated by strain engineering, opening opportunities for applications in spintronic and piezoelectric devices.