We demonstrate that stacking layered materials allows a strain engineering where each layer is strained independently, which we call heterostrain. We combine detailed structural and spectroscopic measurements with tight-binding calculations to show that small uniaxial heterostrain suppresses Dirac cones and leads to the emergence of flat bands in twisted graphene layers (TGLs). Moreover, we demonstrate that heterostrain reconstructs, much more severely, the energy spectrum of TGLs than homostrain for which both layers are strained identically, a result which should apply to virtually all van der Waals structures opening exciting possibilities for straintronics with 2D materials.

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