Localization and circulating currents in curved graphene devices

TL;DR

This paper investigates how curvature in graphene sheets causes unique angular asymmetries in wavefunctions and induces circulating currents that generate measurable local magnetic fields, advancing understanding of curved 2D materials.

Contribution

The study introduces a perturbative approach to analyze energy spectra and eigenstates in curved graphene, revealing curvature-induced circulating currents and their magnetic effects.

Findings

Curvature causes angular asymmetry in wavefunctions.

Circulating currents produce local magnetic fields of about 100 μT.

Theoretical predictions are within measurable range with current technology.

Abstract

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 \textit{real} magnetic fields $\sim$ 100 $\mu$T which can be measured using current technology.