| Summary: | We theoretically study the piezoelectric effects in moirè graphene systems. Since the strain couples to the electrons in the system as an effective vector field, which has opposite signs for the K and K^{′} valleys of graphene, its effects on the two valleys with opposite Chern numbers do not cancel out, but adds up. As a result, some components of the piezoelectric tensor (PET) in these systems, which typically have nontrivial topology in their flat bands, are nearly quantized in terms of the valley Chern numbers. The quantization of the PET is topologically protected by valley U(1) symmetry of the system. Such a conclusion is verified by numerical calculations of the in-plane piezoelectric response of hBN-aligned twisted bilayer graphene (TBG), twisted bilayer-monolayer graphene (TBMG), and twisted double bilayer graphene (TDBG) systems using both continuum model and atomistic tight-binding model. We propose that such nearly quantized piezoelectric response may serve as a direct experimental probe for the valley Chern numbers of the flat bands in moiré graphene systems.
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