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Generating a pure spin current using electrons, which have degrees of freedombeyond spin, such as electric charge and valley index, presents challenges. Inresponse, we propose a novel mechanism based on intervalley exciton dynamics in{\em arc-shaped} strained transition metal dichalcogenides (TMDs) to achievethe {\em exciton spin Hall effect} in an electrically insulating regime,without the need for an external electric field. The interplay between straingradients and strain-induced pseudomagnetic fields results in a net Lorentzforce on long-lived intervalley excitons in WSe$_2$, carrying non-zero spinangular momentum. This process generates an exciton-mediated pure spin Hallcurrent, resulting in opposite-sign spin accumulations and local magnetizationon the two sides of the single-layer arc-shaped TMD. We demonstrate that themagnetic field induced by spin accumulation, at approximately $\sim {\rm mT}$,can be detected using techniques such as superconducting quantum interferencemagnetometry or spatially-resolved magneto-optical Faraday and Kerr rotations.

Exciton Spin Hall Effect In Arc-Shaped Strained WSe$_2$