Strain-Driven "Sinusoidal" Valley Control of Hybridized $Γ-\mathrm{K}$ Excitons

The photoluminescence (PL) of momentum-indirect $\rm Γ- K$ excitons in monolayer WS$_2$ under biaxial strain was recently observed by Blundo et al. [Phys. Rev. Lett. 129, 067402 (2022)], yet its microscopic origin remains elusive. Here we develop a unified framework that reproduces the measured PL and reveals its fundamental excitonic mechanism. We reveal that: (i) the PL originates from genuinely hybridized direct-indirect excitonic eigenstates, rather than nominally mixed species with fixed dominant character; (ii) the direct exciton converts into the indirect one via a previously unrecognized two-step pathway -- exchange-interaction-driven exciton transfer followed by a spin flip; and (iii) a higher-energy indirect exciton, absent from prior studies, acts as a crucial intermediate mediating this conversion. Beyond explaining experiment, our theory predicts a striking strain-driven "sinusoidal'' valley response, furnishing a continuously tunable valley dial that far exceeds binary control schemes. This unified picture of strain-engineered direct-indirect exciton dynamics introduces a new paradigm for manipulating long-lived valley degrees of freedom, opening a pathway toward programmable valley pseudospin engineering and next-generation valleytronic quantum technologies.

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