Localization and circulating currents in curved graphene devices

We calculate the energy spectrum and eigenstates of a graphene sheet which contains a circular deformation. Using time-independent perturbation theory with the ratio of the height and width of the deformation as the small parameter, we find that due to the curvature the wavefunctions for the various states acquire unique angular asymmetry. We demonstrate that the pseudo-magnetic fields induced by the curvature result in circulating probability currents. These circulating currents in turn produce local $\mathit{\text{real}}$ magnetic fields $\sim$ 100 $\mu$T which can be measured using current technology.