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We study the exciton condensate (EC) in a bilayer two-dimension-electron-gas(2DEG) adjacent to a type-II superconductor thin film with an array of pinnedvortex lattices. By applying continuum low energy theory and carrying numericalsimulations of lattice model within mean-field approximation, we find that ifthe order parameter of EC has a vortex profile, there are exact zero modes andassociated \emph{rational} fractional charge for zero pseudospin potential($\mu$) and average chemical potential ($h$): $\mu$=0 and $h$=0; while for$\mu\mathtt{\neq}0$ and $h$=0, intervalley mixing splits the zero energylevels, and the system exhibits \emph{irrational} fractional \emph{axial}charge.

Exciton condensation and fractional charge in a bilayer two-dimension electron gas adjacent to a superconductor film