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Flat electronic bands with tunable structures offer opportunities for theexploitation and manipulation of exotic interacting quantum states. Here, wepresent a controllable route to construct easily tunable flat bands in foldedgraphene, by nano origami-controlled strain engineering, and discovercorrelated states in this system. Via tearing and folding graphene monolayer atarbitrary step edges with scanning tunneling microscope manipulation, we createstrain-induced pseudo-magnetic fields as well as resulting flat electronicbands in the curved edges of folded graphene. We show that the intensity of thepseudo-magnetic field can be readily tuned by changing the width of the foldingedge due to the edge-width-dependent lattice deformation, leading to the welladjustability of the geometry of flat bands in folded graphene. Furthermore, bycreating expected dispersionless flat bands using this technique, thecorrelation-induced splits of flat bands are successfully observed in thedensity of states when these bands are partially filled. Our experimentprovides a feasible and effective pathway to engineer the system with tunableflat band structures, and establishes a new platform that can be used torealize devisable strain and interaction induced quantum phases.

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