Vortex lattice states of bilayer electron-hole fluids in quantizing magnetic fields

We show that the ground state of a weakly charged two-dimensional electron-hole fluid in a strong magnetic field is a broken translation symmetry state with interpenetrating lattices of localized vortices and antivortices in the electron-hole-pair field. The vortices and antivortices carry fractional charges of equal sign but unequal magnitude and have a honeycomb lattice structure that contrasts with the triangular lattices of superconducting electron-electron-pair vortex lattices. We predict that increasing charge density or weakening magnetic field drives a vortex delocalization transition that would be signaled experimentally by an abrupt increase in counterflow transport resistance.