Vortices, Zero Modes, and Fractionalization in the Bilayer-Graphene Exciton Condensate

A real-space formulation is given for the recently discussed exciton condensate in a symmetrically biased graphene bilayer. We show that in the continuum limit an oddly quantized vortex in this condensate binds exactly one zero-mode per valley index of the bilayer. In the full lattice model, the zero modes are split slightly due to intervalley mixing. We support these results by an exact numerical diagonalization of the lattice Hamiltonian. We also discuss the effect of the zero modes on the charge content of these vortices and deduce some of their interesting properties.