Finite-size version of the excitonic instability in graphene quantum dots

TL;DR

This paper investigates the finite-size excitonic instability in graphene quantum dots using various theoretical methods, revealing the importance of electron-hole pair production at strong Coulomb interactions and its relation to bulk excitonic phenomena.

Contribution

It introduces a comprehensive analysis of excitonic instability in finite graphene quantum dots, comparing different theoretical approaches and highlighting the role of electron-hole pairs at strong interactions.

Findings

Electron-hole pair production becomes significant for Coulomb strength .

Finite-size effects mimic bulk excitonic instability phenomena.

Magnetic field effects are also examined.

Abstract

By a combination of Hartree-Fock simulations, exact diagonalization, and perturbative calculations, we investigate the ground-state properties of disorder-free circular quantum dots formed in a graphene monolayer. Taking the reference chemical potential at the Dirac point, we study N \leq 15 interacting particles, where the fine structure constant {\alpha} parametrizes the Coulomb interaction. We explore three different theoretical concepts: (i) Sucher's positive projection ("no-pair") approach, (ii) a more general Hamiltonian conserving both N and the number of additional electron-hole pairs, and (iii) the full quantum electrodynamics (QED) problem, where only N is conserved. We find that electron-hole pair production is important for {\alpha} 1. This corresponds to a reconstruction of the filled Dirac sea and is a finite-size version of the bulk excitonic instability. We also address the effects of an orbital magnetic field.