Graphene kirigami as a platform for stretchable and tunable quantum dot arrays

The quantum transport properties of a graphene kirigami similar to those studied in recent experiments are calculated in the regime of elastic, reversible deformations. Our results show that, at low electronic densities, the conductance profile of such structures replicates that of a system of coupled quantum dots, characterized by a sequence of minibands and stopgaps. The conductance and I-V curves have different characteristics in the distinct stages of deformation that characterize the elongation of these structures. Notably, the effective coupling between localized states is strongly reduced in the small elongation stage but revived at large elongations that allow the reestablishment of resonant tunneling across the kirigami. This provides an interesting example of interplay between geometry, strain, spatial confinement, and electronic transport. The alternating miniband and stopgap structure in the transmission leads to I-V characteristics with negative differential conductance in well defined energy/doping ranges. These effects should be stable in a realistic scenario that includes edge roughness and Coulomb interactions, as these are expected to further promote localization of states at low energies in narrow segments of graphene nanostructures.