  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 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 pseudo-magnetic fields as well as resulting flat electronic
bands in the curved edges of folded graphene. We show that the intensity of the
pseudo-magnetic 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 establishes a new platform that can be used to
realize devisable strain and interaction induced quantum phases.
