The valley degree of freedom in tetragonal systems, governed by crystalline symmetry rather than time-reversal symmetry, offers a distinct paradigm for valleytronics compared to hexagonal systems. Combining symmetry-adapted tight-binding and first-principles calculations, we investigate strain-engineered valley physics in tetragonal monolayers featuring ${\mathit{C}}_{4z}$ and ${\mathit{S}}_{4z}$ symmetries. We unveil that the intrinsic valley-layer coupling within ${\mathit{S}}_{4z}$ symmetric systems, together with a giant bipolar out-of-plane piezoelectric response, enables significant and reversible valley polarization under bipolar in-plane uniaxial strain in the ${\text{Hf}}_2{\text{SiCO}}_2$ monolayer. This phenomenon arises from the interplay between strain-modified hopping integrals and the resulting crystal field potential, distinguishing it from traditional electric-field-driven mechanisms. Furthermore, the symmetry-allowed valley-contrasting linear dichroism under applied strain is notably robust. Our findings highlight strain-direction selectivity as a powerful strategy for achieving and controlling valley polarization, providing a general theoretical framework for mechanovalleytronics in tetragonal systems.

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• Electrical properties
• Piezoelectricity
• Valleytronics
• First-principles calculations