Analytic theory of pair distribution functions in symmetric electron-electron and electron-hole bilayers

TL;DR

This paper develops a self-consistent analytic theory for pair correlation functions in symmetric electron-electron and electron-hole bilayers, accurately matching quantum Monte Carlo data and revealing signs of phase transitions at strong coupling.

Contribution

It introduces a novel analytic approach combining Bose-like and Fermi terms to model correlations, achieving quantitative agreement with DMC data across various conditions.

Findings

Good agreement with Quantum Diffusion Monte Carlo data.

Identification of inter-layer oscillations indicating phase transitions.

Highlighting the importance of three-body correlations at strong coupling.

Abstract

We present a self-consistent analytic theory of the intra-layer and inter-layer pair correlation functions in electron-electron and electron-hole fluid bilayer systems. Our approach involves the solution of a zero-energy scattering Schroedinger equation with an effective potential which includes a Bose-like term from Jastrow-Feenberg correlations and a Fermi term from kinetic energy and exchange, tailored to yield the Hartree-Fock limit at high carrier density. The theory is also shown to satisfy the plasmon sum rule and the charge neutrality condition. We obtain good agreement with the available Quantum Diffusion Monte Carlo (DMC) data in symmetric bilayers over a wide range of carrier density and layer spacing, and stress the role of three-body correlation terms in yielding fully quantitative agreement at strong coupling. Signals of impending transitions to density-modulated states at strong coupling and low layer spacing appear in the calculated pair correlations through inter-layer in-phase oscillations for electron-hole bilayers and out-of-phase oscillations for electron-electron bilayers, in agreement with the DMC findings.