Crossover between the Dense Electron-Hole Phase and the BCS Excitonic Phase in Quantum Dots

TL;DR

This paper investigates the transition between high-density electron-hole plasma and BCS excitonic phases in quantum dots using advanced computational methods, revealing a crossover at a specific density related to exciton packing.

Contribution

It introduces a combined computational approach to study ground-state energies and identifies the crossover density between two distinct quantum phases in quantum dots.

Findings

Energy scales with N and confinement strength

Crossover occurs at four times the exciton close-packing density

Method combines perturbation theory, Lipkin-Nogami, and Monte Carlo projection

Abstract

Second order perturbation theory and a Lipkin-Nogami scheme combined with an exact Monte Carlo projection after variation are applied to compute the ground-state energy of $6\le N\le 210$ electron-hole pairs confined in a parabolic two-dimensional quantum dot. The energy shows nice scaling properties as N or the confinement strength is varied. A crossover from the high-density electron-hole phase to the BCS excitonic phase is found at a density which is roughly four times the close-packing density of excitons.