Unraveling intrinsic flexoelectricity in twisted double bilayer graphene

Moir\'e superlattices of two-dimensional (2D) materials with a small twist angle are thought to exhibit appreciable flexoelectric effect, though unambiguous confirmation of their flexoelectricity is challenging due to artifacts associated with commonly used piezoresponse force microscopy (PFM). For example, unexpectedly small phase contrast ($\sim$$8^{\circ}$) between opposite flexoelectric polarizations was reported in twisted bilayer graphene (tBG), though theoretically predicted value is $180^{\circ}$. Here we developed a methodology to extract intrinsic moir\'e flexoelectricity using twisted double bilayer graphene (tDBG) as a model system, probed by lateral PFM. For small twist angle samples, we found that a vectorial decomposition is essential to recover the small intrinsic flexoelectric response at domain walls from a large background signal. The obtained three-fold symmetry of commensurate domains with significant flexoelectric response at domain walls is fully consistent with our theoretical calculations. Incommensurate domains in tDBG with relatively large twist angles can also be observed by this technique. Our work provides a general strategy for unraveling intrinsic flexoelectricity in van der Waals moir\'e superlattices while providing insights into engineered symmetry breaking in centrosymmetric materials.