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

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