2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143228We investigate the ground state of a balanced electron-hole system in the quantum Hall regime using mean-field theory and obtain a rich phase diagram as a function of interlayer distance d and the filling factor within a layer. We identify an excitonic condensate phase, an excitonic supersolid phase, as well as uncorrelated Wigner crystal states. We find that balanced electron-hole system exhibits a supersolid phase a wide range of filling factors, with different crystal structure ground states. We obtain the ground state stiffness in the excitonic phases and show that the phase transitions from a uniform condensate to a supersolid is accompanied by a marked change in the stiffness. Our results provide the first semi-quantitative determination excitonic supersolid phase diagram and properties.5 pages, 4 figuresMesoscale and Nanoscale PhysicsOther Condensed Mattertext