Valley Emission and Upconversion in Isotopically Engineered Monolayer WS$_2$ under Resonant Excitation

In the quest to optimize the optoelectronic and valleytronic properties of 2D materials, various strategies such as strain engineering, doping, and heterostructuring have been explored. In this direction, isotope engineering also offers a potential avenue to alter electron-phonon interaction and impact quasiparticle scattering processes. In this study, we investigate the dependence of sulfur isotopes on upconversion and valley scattering phenomena by collecting the resonance photoluminescence (PL) under an applied magnetic field from 0 to 14 T at 4 K for the chemical vapor deposition-grown monolayer (1L) of W$^{N}$S$_2$, W$^{32}$S$_2$, and W$^{34}$S$_2$. The upconversion of the mixed-state sulfur 1L (W$^{N}$S$_2$) exhibits one M-phonon absorption, with an obtained optical gain of nearly 30 meV, while the pure sulfur isotope labelled 1Ls (W$^{32}$S$_2$ and W$^{34}$S$_2$) require two phonons (M and $\Gamma$), yielding a gain of around 80 meV. It is also found that the exciton degree of polarization (DOP) of W$^{N}$S$_2$ changes significantly by $\sim$ -30$\%$ as the field increases from 0 to 14 T, while for W$^{32}$S$_2$ and W$^{34}$S$_2$, the exciton DOP increases by up to $\sim$ 8$\%$. Similarly, distinct changes in the DOP are observed for trions and localized excitons among all the samples, attributed to the different valley scattering phenomena. The 1L W$^{N}$S$_2$ demonstrates a combination of intraband and interband scattering, whereas in the case of W$^{32}$S$_2$ intraband scattering is preferred; W$^{34}$S$_2$ predominantly exhibits interband scattering. Finally, a phenomenological model is proposed to describe the upconversion and valley scattering processes.