NanoVelcro: Theory of Guided Folding in Atomically Thin Sheets with Regions of Complementary Doping

Abstract

Folding has been commonly observed in two-dimensional materials such as graphene and monolayer transition metal dichalcogenides. Although interlayer coupling stabilizes these folds, it provides no control over the placement of the fold, let alone the final folded shape. Lacking nanoscale "fingers" to externally guide folding, control requires interactions engineered into the sheets that guide them toward a desired final folded structure. Here we provide a theoretical framework for a general methodology toward this end: atomically thin 2D sheets are doped with patterns of complementary n-type and p-type regions whose preferential adhesion favors folding into desired shapes. The two-colorable theorem in flat-foldable origami ensures that arbitrary folding patterns are in principle accessible to this method. This complementary doping method can be combined with nanoscale crumpling (by, for example, passage of 2D sheets through holes) to obtain not only control over fold placements but also the ability to distinguish between degenerate folded states, thus attaining nontrivial shapes inaccessible to sequential folding.

Atomically precise, custom-design origami graphene nanostructures

“…Origami, the ancient art of paper folding, has been widely used in diverse areas, from architecture to battery design and DNA nanofabrication (10). It has also inspired the fabrication or simulation of macroscale origami graphene structures and devices (11)(12)(13)(14)(15)(16)(17)(18)(19)(20), even machines (21). Nano-scale graphene origami, however, in which quantum phenomena are expected to be manifest, has been mainly the realm of theoretical investigations, predicting GNSs with unusual physical properties such as an ability to carry spin-polarized currents for spintronic applications (22), foldinduced gauge fields (23), large permanent electric dipoles (24), strong magnetophotoelectric effect (25), and topologically protected fold states (26).…”

Atomistic simulations of graphene origami: Dynamics and kinetics

“…[14] Previous studies reported that graphene could be folded by a contact-free atomic force microscope (AFM) tip [15] or scanning tunneling microscope (STM) tip. [16,17] In addition, graphene origami occurs with external stimuli such as temperature, [18][19][20] light, [21] strain, [2,22] doping, [23] solvent, [24] and also spontaneously due to the formation of joint edges in the growth process. [25] Chen et al realized the atomically precise and direction-controllable folding of graphene nano island (GNI) using an STM tip at ultra-low temperature.…”

Plasmonic properties of folded graphene nanodisks

“…It is a way of building 3D devices based on 2D materials. Thus, it has already stimulated the development of simulation and fabrication of folded graphene structures and devices [18][19][20][21][22][23][24][25][26][27], and origami machines [28]. Considerable effort devoted to achieving folded graphene structures can be traced back to 1995 by Ebbesen and Hiura, who were first envisioned 'Graphite origami', and they observed the folding of graphite surface layers with accidental tearing through an atomic force microscope tip [29].…”