Beyond the random phase approximation in electron-hole bilayer superfluidity
Phys. Rev. B 114, 034508 – Published 20 July, 2026
DOI: https://doi.org/10.1103/sly5-v467
Abstract
We derive the normal and anomalous proper polarization functions and the screened Coulomb interactions in a two-dimensional superfluid electron-hole bilayer, including all first-order corrections beyond the Random Phase Approximation (RPA) at zero temperature. This requires a modification of the perturbation method as first noted by Nozières and Schrieffer. We discuss the physical origin and magnitude of the first-order corrections in a superfluid system with long-range Coulomb interactions. The screened electron-electron, hole-hole, and electron-hole interactions in the superfluid state are evaluated as functions of the carrier density. We find that at low density, the strong cancellations between the normal and anomalous components that make screening of the interactions negligible, apply not only within RPA but also with the first-order corrections included. As the density is increased, the normal-anomalous cancellation weakens and screening becomes increasingly significant. We find that the first-order corrections amplify the normal-anomalous difference but only at large momenta exchanged in the two-particle scattering, so their effect on the interactions remains modest. We conclude that the superfluid state RPA is an excellent approximation for the screening and for the effective electron-hole pairing in this superfluid system over the range of densities up to the maximum of the superfluid gap.
