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Egger, R.; De Martino, A.; Siedentop, H.; Stockmeyer, E. (2010)
Languages: English
Types: Article
Subjects: QC, Mathematical Physics, Condensed Matter - Mesoscale and Nanoscale Physics

Classified by OpenAIRE into

arxiv: Physics::Chemical Physics, Physics::Atomic and Molecular Clusters, Computer Science::Other, Physics::Classical Physics
We study the energy of quasi-particles in graphene within the Hartree-Fock approximation. The quasi-particles are confined via an inhomogeneous magnetic field and interact via the Coulomb potential. We show that the associated functional has a minimizer and determines the stability conditions for the N-particle problem in such a graphene quantum dot.
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    • [1] Geim A K and Novoselov K S 2007 The rise of graphene Nature Materials 6 183-191
    • [2] Castro Neto A H, Guinea F, Peres N M R, Novoselov K S and Geim A K 2009 The electronic properties of graphene Rev. Mod. Phys. 81 109-162
    • [3] Geim A K 2009 Graphene: Status and prospects Science 324 1530-1534
    • [4] Reimann S M and Manninen M 2002 Electronic structure of quantum dots Rev. Mod. Phys. 74 1283-1342
    • [5] Pereira J M, Mlinar V, Peeters F M and Vasilopoulos P 2006 Confined states and directiondependent transmission in graphene quantum wells Phys. Rev. B 74 045424/1-5
    • [6] Silvestrov P G and Efetov K B 2007 Quantum dots in graphene Phys. Rev. Lett. 98 016802/1-4
    • [7] Chen H-Y, Apalkov V and Chakraborty T 2007 Fock-Darwin states of Dirac electrons in graphene-based artificial atoms Phys. Rev. Lett. 98 186803/1-4
    • [8] Matulis A and Peeters F M 2008 Quasibound states of quantum dots in single and bilayer graphene Phys. Rev. B 77 115423/1-7
    • [9] Recher P, Nilsson J, Burkard G and Trauzettel B 2009 Bound states and magnetic field induced valley splitting in gate-tunable graphene quantum dots Phys. Rev. B 79 085407/1-11
    • [10] De Martino A, Dell'Anna L and Egger R 2007 Magnetic confinement of massless Dirac fermions in graphene Phys. Rev. Lett. 98 066802/1-4
    • [11] H¨ausler W and Egger R 2009 Artificial atoms in interacting graphene quantum dots Phys. Rev. B 80 161402(R)/1-4
    • [12] Stampfer C, Gu¨ttinger J, Molitor F, Graf D, Ihn T and Ensslin K 2008 Tunable Coulomb blockade in nanostructured graphene Appl. Phys. Lett. 92 012102/1-3
    • [13] Cerchez M, Hugger S, Heinzel T and Schulz N 2007 Effect of edge transmission and elastic scattering on the resistance of magnetic barriers: Experiment and theory Phys. Rev. B 75 035341/1-6
    • [14] Reijniers J, Peeters F M and Matulis A 1999 Quantum states in a magnetic antidot Phys. Rev. B 59 2817-2823
    • [15] Sucher J 1980 Foundations of the relativistic theory of many-electron atoms Phys. Rev. A 22 348-362
    • [16] Sucher J 1984 Foundations of the relativistic theory of many-electron bound states Int. J. Quantum Chem. 25 3-21
    • [17] Sucher J 1987 Relativistic many-electron Hamiltonians Phys. Scripta 36 271-281
    • [18] Hainzl C, Lewin M and Seiringer R 2008 A nonlinear model for relativistic electrons at nonzero temperature Rev. Math. Phys. 20 1283-1307
    • [19] Reiher M and Wolf A 2009 Relativistic Quantum Chemistry: The Fundamental Theory of Molecular Science (Weinheim: Wiley-VCH)
    • [20] Weidmann J 2000 Linear Operatoren in Hilbertra¨umen, Vol. I: Grundlagen (Stuttgart: Teubner Verlag)
    • [21] Reed M and Simon B 1975 Methods of Modern Mathematical Physics, Vol. II: Fourier Analysis and Self-Adjointness (Academic Press)
    • [22] Giuliani G F and Vignale G 2005 Quantum Theory of the Electron Liquid (Cambridge: Cambridge University Press)
    • [23] Lieb E H, Siedentop H and Solovej J P 1997 Stability of relativistic matter with magnetic fields Phys. Rev. Lett. 79 1785-1788
    • [24] Mu¨ller A M K 1984 Explicit approximate relation between reduced two- and one-particle density matrices Phys. Lett. A 105 446-452
    • [25] Frank R L, Lieb E H, Seiringer R and Siedentop H 2007 Mu¨ller's exchange-correlation energy in density-matrix-functional theory Phys. Rev. A 76 052517/1-16
    • [26] Frank R L, Lieb E H and Seiringer R 2007 Stability of relativistic matter with magnetic fields for nuclear charges up to the critical value Comm. Math. Phys. 275 479-489
    • [27] Barbaroux J-M, Farkas W, Helffer B and Siedentop H 2005 On the Hartree-Fock equations of the electron-positron field Comm. Math. Phys. 255 131-159
    • [28] Bach V 1992 Error bound for the Hartree-Fock energy of atoms and molecules Comm. Math. Phys. 147 527-548
    • [29] Lieb E H and Simon B 1977 The Hartree-Fock theory for Coulomb systems Comm. Math. Phys. 53 185-194
    • [30] Solovej J P 1991 Proof of the ionization conjecture in a reduced Hartree-Fock model Inventiones Math. 104 291-311
    • [31] Kato T 1966 Perturbation theory for linear operators, vol. 132 of Grundlehren der mathematischen Wissenschaften (Berlin: Springer Verlag)
    • [32] Lions J.-L. and Magenes E 1972 Non-homogeneous boundary value problems and applications Vol. I (New York: Springer Verlag).
    • [33] De Martino A and Egger R 2010 On the spectrum of a magnetic quantum dot in graphene Semicond. Science Techn. 25 034006/1-4
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