Valley piezoelectricity promoted by spin-orbit coupling in quantum materials

Quantum materials have exhibited attractive electro-mechanical responses,but their piezoelectric coefficients are far from satisfactory due to the lack of feasible strategies to benefit from the quantum effects.We discovered the valley piezoelectric mechanism that is absent in the traditional piezoelectric theories yet promising to overcome this challenge.A theoretical model was developed to elucidate the valley piezoelectricity in 2D materials as originating from the strong spin-orbit coupling.Consistent analytical and density-functional-theory calculations validate the model and unveil the crucial dependence of valley piezoelectricity on valley/spin splitting and hybridization energy.Up to 50%of electro-mechanical responses in our tested twodimensional systems are attributed to the valley piezoelectric mechanisms.Rational strategies including doping,passivation,and external strain are proposed to optimize piezoelectricity,with a more than 127%increase in piezoelectricity demonstrated by density-functional-theory simulations.The general valley piezoelectric model not only opens an opportunity to achieve outstanding piezoelectricity via optimizing intrinsic variables but also makes the large family of valley materials promising for piezoelectric sensing and energy harvesting.