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 pinned vortex lattices. By applying continuum low energy theory and carrying numerical simulations of lattice model within mean-field approximation, we find that if the order parameter of EC has a vortex profile, there are exact zero modes and associated \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 energy levels, and the system exhibits \emph{ irrational} fractional \emph{ axial} charge.
Categories: cond-mat.mes-hall