Electronic properties of graphene quantum ring with wedge disclination

We study the energy spectrum and persistent current of charge carriers confined in a graphene quantum ring geometry radius $R$ width $w$ subjected to magnetic flux. consider case where crystal symmetry is locally modified by replacing hexagon pentagon, square, heptagon or octagon. To model this type defect we include appropriate boundary conditions for angular coordinate. The electrons are finite strip radial direction setting infinite mass at edges strip. solutions expressed terms Hankel functions their asymptotic behavior allows derive quantized levels presence an gap. also investigate currents that appear how wedge disclination influences different transport quantities.