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.

Moiré superlattices in graphene supported on various substrates have opened a new avenue to engineer graphene's electronic properties. Yet, the exact crystallographic structure on which their band structure depends remains highly debated. In this scanning tunneling microscopy and density functional theory study, we have analysed graphene samples grown on multilayer graphene prepared onto SiC and on the close-packed surfaces of Re and Ir with ultra-high precision. We resolve small-angle twists and shears in graphene, and identify large unit cells comprising more than 1,000 carbon atoms and exhibiting nontrivial nanopatterns for moiré superlattices, which are commensurate to the graphene lattice. Finally, a general formalism applicable to any hexagonal moiré is presented to classify all reported structures.Graphene (gr) is a two-dimensional crystal with honeycomb structure, whose peculiar electronic properties have raised considerable interest in the past few years. Indeed, its electronic bands cross at the K and K′ corners of the Brillouin zone, giving rise to a linear energy dispersion of its quasiparticles close to the Fermi level 1 . Moreover, the bipartite nature of graphene's lattice, with two triangular carbon sub-lattices (A and B), confers unique properties to these quasiparticles. By analogy to quantum electrodynamics 2 , a sublattice-related quantum number, so-called pseudo-spin, equivalent to the spin of Dirac fermions is defined 3 . For these reasons, the conical electronic bands around the K and K′ points of the Brillouin zone are called Dirac cones.Such exotic electronic properties are predicted for pristine graphene, but are altered when graphene is supported by a substrate. Indeed, due to the structural mismatch between graphene and its support, graphene has periodically varying stacking configurations with its substrate 4-9 . This effect modulates the graphene-substrate interaction and distance [10][11][12][13][14] , over a so-called moiré periodicity, which can range from ~1 to ~15 nm. Depending on the interaction between graphene and the substrate, the moiré can have a dramatic impact on graphene's properties. Some substrates impose only a weak interaction dominated by van der Waals forces, which is the case for graphene on hexagonal boron nitride 15 or multilayer graphene on the carbon face of SiC 16 . In this case, the graphene-substrate distance is about 3.4 Å (refs 16,17), very close to the value 3.3539 Å of highly oriented pyrolytic graphite (HOPG) 18 , and graphene's electronic properties are mostly preserved 17,19 . In these systems, the moiré acts as a smooth superpotential that varies slowly compared to the one associated to carbon atoms. The corresponding unit cell, which is larger than the one of pristine graphene, is associated with replica Dirac cones, reduced Fermi velocity [20][21][22][23] , with either superlattice Dirac cones 21,22,24,25 or mini-gaps 20,26 at the moiré Brillouin zone boundary. Such properties make this system an ideal playground to investigate quantum phases ar...