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16 February 2025
 
  » arxiv » 1109.0174

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Finite-size version of the excitonic instability in graphene quantum dots
Tomi Paananen ; Reinhold Egger ;
Date 1 Sep 2011
AbstractBy 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.
Source arXiv, 1109.0174
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