Vortex and gap generation in gauge models of graphene

Effective quantum field theoretical continuum models for graphene are investigated. The models include a complex scalar field and a vector gauge field. Different gauge theories are considered and their gap patterns for the scalar, vector, and fermion excitations are investigated. Different gauge groups lead to different relations between the gaps, which can be used to experimentally distinguish the gauge theories. In this class of models the fermionic gap is a dynamic quantity. The finite-energy vortex solutions of the gauge models have the flux of the magnetic field quantized, making the Bohm-Aharonov effect active even when external electromagnetic fields are absent. The flux comes proportional to the scalar field angular momentum quantum number. The zero modes of the Dirac equation show that the gauge models considered here are compatible with fractionalization.