Persistence of zero modes in a gauged Dirac model for bilayer graphene

A recently constructed model for low-lying excitations in bilayer graphene exhibits midgap, zero-energy modes in its Dirac-type spectrum when a scalar order parameter takes a vortex profile. We show that these modes persist when the dynamics is extended by a gauge field interaction, which also renders finite the vortex energy. The effect of the gauge field on the zero-energy wave function is to shift the phase of the (damped) oscillatory component of the wave function in the absence of the gauge field.