Generation mechanism of energy gaps between conductance and valence bands is at the centre of the study of graphene material. Recently Chamon, Jackiw, et al. proposed a mechanism of using a Kekul\'{ e} distortion background field $% \varphi $ and its induced gauge potential $A_{ i}$ to generate energy gaps. In this paper various vortex structures inhering in this model are studied. Regarding $\varphi $ as a generic background field rather than a fixed Nielson-Oleson type distribution, we have found two new types of vortices on the graphene surface --- the velocity field vortices and the monopole-motion induced vortices --- from the inner structure of the potential $A_{ i}$. These vortex structures naturally arise from the motion of the Dirac fermions instead of from the background distortion field.
Categories: cond-mat.mes-hall math-ph math.MP