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

Conference paper
Part of the NATO Science for Peace and Security Series B: Physics and Biophysics book series (NAPSB)

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.

Keywords

Dirac Point Graphene Monolayer Exact Diagonalization Magnetic Catalysis Interaction Matrix Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Geim AK, Novoselov KS (2007) Nat Mater 6:183ADSCrossRefGoogle Scholar
  2. 2.
    Castro Neto AH, Guinea F, Peres NMR, Novoselov KS, Geim A (2009) Rev Mod Phys 81:109ADSCrossRefGoogle Scholar
  3. 3.
    Kotov VN, Uchoa B, Pereira VM, Castro Neto AH, Guinea F (2012) Rev Mod Phys 84:1067ADSCrossRefGoogle Scholar
  4. 4.
    Hasan MZ, Kane CL (2010) Rev Mod Phys 82:3045ADSCrossRefGoogle Scholar
  5. 5.
    González J, Guinea F, Vozmediano MAH (2001) Phys Rev B 63:134421ADSCrossRefGoogle Scholar
  6. 6.
    Khveshchenko DV (2009) J Phys Condens Matter 21:075303ADSCrossRefGoogle Scholar
  7. 7.
    Son DT (2007) Phys Rev B 75:235423ADSCrossRefGoogle Scholar
  8. 8.
    Müller M, Schmalian J, Fritz L (2009) Phys Rev Lett 103:025301ADSCrossRefGoogle Scholar
  9. 9.
    Drut JE, Lähde TA (2009) Phys Rev Lett 102:026802; (2009) Phys Rev B 79:165425Google Scholar
  10. 10.
    Gamayun OV, Gorbar EV, Gusynin VP (2010) Phys Rev B 81:075429; (2011) Phys Rev B 83:235104Google Scholar
  11. 11.
    Wang J, Fertig HA, Murthy G, Brey L (2011) Phys Rev B 83:035404ADSCrossRefGoogle Scholar
  12. 12.
    Greiner W, Müller B, Rafelski J (1985) Quantum electrodynamics of strong fields. Springer, BerlinCrossRefGoogle Scholar
  13. 13.
    Gusynin VP, Miransky VA, Shovkovy IA (1994) Phys Rev Lett 73:3499ADSCrossRefGoogle Scholar
  14. 14.
    Paananen T, Egger R (2012) Phys Rev B 84:155456ADSCrossRefGoogle Scholar
  15. 15.
    Kouwenhoven LP, Austing DG, Tarucha S (2001) Rep Prog Phys 64:701ADSCrossRefGoogle Scholar
  16. 16.
    Reimann SM, Manninen M (2002) Rev Mod Phys 74:1283ADSCrossRefGoogle Scholar
  17. 17.
    Ponomarenko LA, Schedin F, Katsnelson MI, Yang R, Hill EW, Novoselov KS, Geim AK (2008) Science 320:356ADSCrossRefGoogle Scholar
  18. 18.
    Todd K, Chou HT, Amasha S, Goldhaber-Gordon D (2009) Nano Lett 9:416ADSCrossRefGoogle Scholar
  19. 19.
    Ritter KA, Lyding JW (2009) Nat Mater 8:235ADSCrossRefGoogle Scholar
  20. 20.
    Güttinger J, Stampfer C, Libisch F, Frey T, Burgdorfer J, Ihn T, Ensslin K (2009) Phys Rev Lett 103:046810ADSCrossRefGoogle Scholar
  21. 21.
    Güttinger J, Frey T, Stampfer C, Ihn T, Ensslin K (2010) Phys Rev Lett 105:116801ADSCrossRefGoogle Scholar
  22. 22.
    Berry MV, Mondragon RJ (1987) Proc R Soc Lond A 412:53MathSciNetADSCrossRefGoogle Scholar
  23. 23.
    Schnez S, Ensslin K, Sigrist M, Ihn T (2008) Phys Rev B 78:195427ADSCrossRefGoogle Scholar
  24. 24.
    Wunsch B, Stauber T, Guinea F (2008) Phys Rev B 77:035316ADSCrossRefGoogle Scholar
  25. 25.
    Ezawa M (2008) Phys Rev B 77:155411ADSCrossRefGoogle Scholar
  26. 26.
    Egger R, De Martino A, Siedentop H, Stockmeyer E (2010) J Phys A Math Theor 43:215202ADSCrossRefGoogle Scholar
  27. 27.
    Paananen T, Egger R, Siedentop H (2011) Phys Rev B 83:085409ADSCrossRefGoogle Scholar
  28. 28.
    Brown GE, Ravenhall DG (1951) Proc R Soc Lond A 208:552MathSciNetADSMATHCrossRefGoogle Scholar
  29. 29.
    Sucher J (1957) Phys Rev 107:1448; (1958) Phys Rev 109:1010; (1980) Phys Rev A 22:348; (1984) Int J Quantum Chem 25:3Google Scholar
  30. 30.
    Häusler W, Egger R (2009) Phys Rev B 80:161402(R)Google Scholar
  31. 31.
    Grabert H, Devoret MH (eds) (1992) Single charge tunneling, vol 294, NATO ASI series B, physics. Plenum Press, New YorkGoogle Scholar
  32. 32.
    Reiher M, Wolf A (2009) Relativistic quantum chemistry. Wiley VCH, WeinheimCrossRefGoogle Scholar
  33. 33.
    Mittleman MH (1981) Phys Rev A 24:1167ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  1. 1.Faculty of PhysicsUniversitat Bielefeld, FinanzbuchhaltungBielefeldGermany
  2. 2.Institut für Theoretische PhysikHeinrich-Heine-UniversitDüsseldorfGermany

Personalised recommendations