Rashba spin-orbit coupling effects on piezoelectric properties of two-dimensional Janus materials

Intriguing piezoelectric phenomena have been reported in various two-dimensional quantum materials, where intrinsic geometric characteristics and spin-orbit coupling (SOC) effects play important roles. However, the role of Rashba SOC in piezoelectric properties remains unclear. Here we develop a theoretical model to elucidate the impact of Rashba SOC on the piezoelectricity of two-dimensional Janus materials. The results suggest that conventional piezoelectricity can be significantly enhanced by Rashba SOC due to increased wave-function localization, which reduces the hopping energy and modulates the effective Berry curvature distribution. First-principles calculations were performed on Janus transition metal dichalcogenides and ${A}_{2}{\mathrm{P}}_{2}{X}_{6}$ ($A$ = Bi, Ga, In; $X$ = S, Se, Te) systems, confirming the dependence of piezoelectricity on Rashba SOC. The conventional piezoelectric coefficient of WSeTe is predicted as 3.62 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}10}$ C/m, which is 40.0% and 98.7% larger than those of $\mathrm{WS}{\mathrm{e}}_{2}$ and $\mathrm{WT}{\mathrm{e}}_{2}$, respectively. Empirical formulas were further derived to reveal the general trends of both conventional and unconventional piezoelectricity in Janus systems with ${C}_{3v}$ symmetry. The extended understanding of the piezoelectric mechanism in quantum materials opens up opportunities for the development of efficient micronano piezotronics and spintronics devices.