"Dilute" excitons in a double layer system: single-exciton and mean-field approach

Double layer systems where one layer has electrons and the holes are in a parallel layer a distance d away are expected to undergo excitonic condensation at low temperature. This excitonic condensate is traditionally described by a many-body wavefunction that encodes the coherence between electron and hole bands. Here we compare the mean-field ground state in the limit of dilute electron (hole) density with the ground state of a single electron-hole pair in double-layer system. As the interlayer distance d increases, we find that the excitonic size, characterized by the width of the momentum-space wavefunction, also increases. By comparing the single-exciton wavefunction with the mean-field analysis, we determine the d-dependence of the "diluteness" of the exciton gas in a balanced double-layer system with given electron (or hole) density.