Electrical control of two-dimensional electron-hole fluids in the quantum Hall regime

We study the influence of quantizing perpendicular magnetic fields on the ground state of a bilayer with electron and hole fluids separated by an opaque tunnel barrier. In the absence of a field, the ground state at low carrier densities is a condensate of s-wave excitons that has spontaneous interlayer phase coherence. We find that a series of phase transitions emerge at strong perpendicular fields between condensed states and incompressible incoherent states with full electron and hole Landau levels. When the electron and hole densities are unequal, condensation can occur in higher angular momentum electron-hole pair states and, at weak fields, break rotational symmetry. We explain how this physics is expressed in dual-gate phase diagrams, and predict transport and capacitively probed thermodynamic signatures that distinguish different states.