Induced fractional valley number in graphene with topological defects

We report on the possibility of valley number fractionalization in graphene with a topological defect that is accounted for in Dirac equation by a pseudomagnetic field. The valley number fractionalization is attributable to an imbalance on the number of one particle states in one of the two Dirac points with respect to the other and it is related to the flux of the pseudomagnetic field. We also discuss the analog effect the topological defect might lead in the induced spin polarization of the charge carriers in graphene.