Helical van der Waals crystals with discretized Eshelby twist

The ability to manipulate the twisting topology of van der Waals structures offers a new degree of freedom through which to tailor their electrical and optical properties. The twist angle strongly affects the electronic states, excitons and phonons of the twisted structures through interlayer coupling, giving rise to exotic optical, electric and spintronic behaviours^1-5. In twisted bilayer graphene, at certain twist angles, long-range periodicity associated with moiré patterns introduces flat electronic bands and highly localized electronic states, resulting in Mott insulating behaviour and superconductivity^3,4. Theoretical studies suggest that these twist-induced phenomena are common to layered materials such as transition-metal dichalcogenides and black phosphorus^6,7. Twisted van der Waals structures are usually created using a transfer-stacking method, but this method cannot be used for materials with relatively strong interlayer binding. Facile bottom-up growth methods could provide an alternative means to create twisted van der Waals structures. Here we demonstrate that the Eshelby twist, which is associated with a screw dislocation (a chiral topological defect), can drive the formation of such structures on scales ranging from the nanoscale to the mesoscale. In the synthesis, axial screw dislocations are first introduced into nanowires growing along the stacking direction, yielding van der Waals nanostructures with continuous twisting in which the total twist rates are defined by the radii of the nanowires. Further radial growth of those twisted nanowires that are attached to the substrate leads to an increase in elastic energy, as the total twist rate is fixed by the substrate. The stored elastic energy can be reduced by accommodating the fixed twist rate in a series of discrete jumps. This yields mesoscale twisting structures consisting of a helical assembly of nanoplates demarcated by atomically sharp interfaces with a range of twist angles. We further show that the twisting topology can be tailored by controlling the radial size of the structure.