Origami-controlled strain engineering of tunable flat bands and correlated states in folded graphene

Flat electronic bands with tunable structures offer opportunities for the exploitation and manipulation of exotic interacting quantum states. Here, we present a controllable route to construct easily tunable flat bands in folded graphene by nano origami-controlled strain engineering, and we discover correlated states in this system. Via tearing and folding graphene monolayer at arbitrary step edges with scanning tunneling microscope manipulation, we create strain-induced pseudomagnetic fields as well as resulting flat electronic bands in the curved edges of folded graphene. We show that the intensity of the pseudomagnetic field can be readily tuned by changing the width of the folding edge due to the edge-width-dependent lattice deformation, leading to the well adjustability of the geometry of flat bands in folded graphene. Furthermore, by creating expected dispersionless flat bands using this technique, the correlation-induced splits of flat bands are successfully observed in the density of states when these bands are partially filled. Our experiment provides a feasible and effective pathway to engineer the system with tunable flat band structures, and it establishes a platform that can be used to realize devisable strain and interaction-induced quantum phases.