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On the Finite-Size Excitonic Instability in Interacting Graphene Quantum Dots

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Low-Dimensional Functional Materials

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Abstract

Using Hartree-Fock simulations, exact diagonalization and perturbative calculations, we study ground-state properties of clean circular quantum dots formed in a graphene monolayer. With chemical potential at the neutrality point, we study N ≤ 15 interacting particles, where the fine structure constant α parametrizes the Coulomb interaction. We explore Sucher’s positive projection (“no-pair”) approach, a more general Hamiltonian conserving both N and the number of additional electron-hole pairs, and the full QED problem, where only N is conserved. We find electron-hole pair production for α > 1, where the filled Dirac sea is reconstructed and a finite-size excitonic instability occurs. We also address the case of an orbital magnetic field.

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Notes

  1. 1.

    In the HF calculations, it is sometimes advantageous to include a small mixing term in the single-particle Hamiltonian, \(H_{\mathrm{mix}} =\delta _{K}\tau _{x} +\delta _{s}s_{x}.\) Inclusion of H mix in the construction of the eigen-energies and -states is straightforward. This allows us to probe all spin and valley states in one run, and by careful extrapolation δ K , δ s  → 0, we can extract the ground state.

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Authors and Affiliations

  1. Faculty of Physics, Universitat Bielefeld, Finanzbuchhaltung, 101133, 33511, Bielefeld, Germany

    Tomi Paananen

  2. Institut für Theoretische Physik, Heinrich-Heine-Universit, D-40225, Düsseldorf, Germany

    Reinhold Egger

Authors
  1. Tomi Paananen
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  2. Reinhold Egger
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Corresponding author

Correspondence to Reinhold Egger .

Editor information

Editors and Affiliations

  1. , Institut für Theoretische Physik IV, Heinrich-Heine-Universität, Universitätsstrasse 1, Düsseldorf, 40225, Germany

    Reinhold Egger

  2. Laboratory for Advanced Studies, Department of Energy, Turin Polytechnic University in Tashkent, Niyazov St. 17, Tashkent, 100174, Uzbekistan

    Davron Matrasulov

  3. , Department of Physics, National University of Uzbekistan, Niyazov St. 17, Tashkent, 100174, Uzbekistan

    Khamdam Rakhimov

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Paananen, T., Egger, R. (2013). On the Finite-Size Excitonic Instability in Interacting Graphene Quantum Dots. In: Egger, R., Matrasulov, D., Rakhimov, K. (eds) Low-Dimensional Functional Materials. NATO Science for Peace and Security Series B: Physics and Biophysics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-6618-1_1

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