Excitonic Condensation in a Symmetric Electron-Hole Bilayer

Using diffusion Monte Carlo simulations we have investigated the ground state of a symmetric electron-hole bilayer and determined its phase diagram at $T=0\mathrm{}$. We find clear evidence of an excitonic condensate, whose stability however is affected by an in-layer electronic correlation. This stabilizes the electron-hole plasma at large values of the density or interlayer distance, and the Wigner crystal at low density and large distance. We have also estimated pair correlation functions and low-order density matrices to give a microscopic characterization of correlations as well as to try and estimate the condensate fraction.