Quadriexciton binding energy in electron-hole bilayers

Excitonic condensation and superfluidity have recently received a renewed attention, due to the fabrication of bilayer systems in which electrons and hole are spatially separated and form stable pairs known as indirect excitons. Dichalcogenides- and graphene- based bilayers are nowadays built and investigated, giving access to systems with (i) only spin degeneracy, (ii) spin and valley degeneracy. Simulation studies performed in the last decade at $T=0$ for simple, model electron-hole bilayers, as function of inter-layer distance and in-layer carrier density, have revealed in case (i) the formation of biexcitons in a tiny region of parameter space and in case (ii) the formation of stable compounds made of 4 electrons and 4 holes (quadriexcitons) in a sizable region of parameter space. Of some interest is the relation of the properties of isolated biexcitons (quadriexcitons) and those of their finite density counterpart. In fact, the isolated biexciton has been repeatedly studied in the last years with simulations and other techniques. No simulations, instead, are available to our knowledge for the isolated quadriexciton, for which we present here results of the first quantum Monte Carlo (QMC) study. Stability with respect to the dissociation into biexcitons, and the pair correlations with varying the inter-layer distance $d$ are discussed.