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

Abstract

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-widthdependent 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.

Mechanical, electronic, optical, piezoelectric and ferroic properties of strained graphene and other strained monolayers and multilayers: an update

“…The effects of the resulting effective gauge potential were seen by dI/dV measurements taken at locations marked by circles in figures 2(e) and (f) [85]. The splitting of dI/dV peaks (and their weight redistribution) in figure 2(g) are manifestations of localised states on folded graphene [82,83].…”

“…The tearing and subsequent folding of the topmost graphitic layer by an STM tip is depicted in figure 2 [82]. There, the tip approaches graphite right before a step edge, moving across it afterwards (figure 2(a)) [82].…”

“…The tearing and subsequent folding of the topmost graphitic layer by an STM tip is depicted in figure 2 [82]. There, the tip approaches graphite right before a step edge, moving across it afterwards (figure 2(a)) [82]. As a result, the tip (i) tears and (ii) folds the uppermost monolayer (figures 2(b)-(d)), creating nonuniform strain at the folded edge.…”

“…One-dimensional electronic bands were created along the longest fold in figure 2(d). There, the axial direction of the fold turned out to be parallel to graphene's armchair direction, and the experimental electronic density [82] was contrasted against a linear chain TB Hamiltonian model, where the strain appears as a modulation of hopping parameters and self-energies [1]. According to the model, the flat bands are topological in nature [86].…”

Electronic transport in graphene with out-of-plane disorder

“…Experimental studies of the electronic transport in graphene with out-of-plane disorder have also been published [6,26]. It was proposed that controlled folding of graphene can be used for engineering charge-carrier dynamics [27][28][29][30]. No question, future applications of graphene in electronics call for a detailed understanding of the effect of this ubiquitous type of disorder on the electronic transport.…”