Realizing and manipulating valley polarization is extremely important to valleytronics. Ferrovalley materials with spontaneous valley polarization are excellent candidates for this purpose. However, for intrinsic ferrovalley materials, ferromagnetism or ferroelectric polarization is usually required, limiting the development of valleytronics, as only systems without inversion symmetry are considered. In this paper, using both group theory analysis and band structure calculations, we demonstrate that valley polarization can exist in systems with both time and space inversion symmetry, and the ferroelastic effect can control the ferrovalley states. Choosing stacking bilayer systems as an example, we achieved valley polarization switching using the shear strain, which uncovers the link between ferrovalley and ferroelasticity. Our investigations not only provide a mechanical way to manipulate valley degree of freedom but also enrich the understanding of the coupling between different ferroic properties.

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• Valley degrees of freedom
• Valleytronics
• Layered crystals
• Density functional theory
• Tight-binding model