Multiparticle equations for interacting Dirac fermions in magnetically confined graphene quantum dots

Egger, Reinhold; Martino, Alessandro De; Siedentop, Heinz; Stockmeyer, Edgardo

doi:10.1088/1751-8113/43/21/215202

Cited by 15 publications

(30 citation statements)

References 33 publications

(81 reference statements)

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“…The numerical algorithm to obtain the HF ground state is standard and can be found, for instance, in Ref. 20…”

Section: B Numerical Approachesmentioning

confidence: 99%

“…We then follow Sucher 29 and confine the Hilbert space to positive-energy eigenstates of the full singleparticle problem, i.e., we assume an inert filled Dirac sea. This projection approach has been successfully employed in the same context before, 19,20 and one can analyze also other values for the chemical potential. The accuracy of this method was carefully assessed in Ref.…”

Section: Introductionmentioning

confidence: 99%

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Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

2011

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We study N interacting massless Dirac fermions confined in a two-dimensional quantum dot. Physical realizations of this problem include a graphene monolayer and the surface state of a strong topological insulator. We consider both a magnetic confinement and an infinite mass confinement. The ground state energy is computed as a function of the effective interaction parameter α from the Hartree-Fock approximation and, alternatively, by employing the Müller exchange functional. For N = 2, we compare those approximations to exact diagonalization results. The Hartree-Fock energies are highly accurate for the most relevant interaction range α 2, but the Müller functional leads to an unphysical instability when α 0.756. Up to 20 particles were studied using HartreeFock calculations. Wigner molecule formation was observed for strong but realistic interactions, accompanied by a rich peak structure in the addition energy spectrum.

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“…The numerical algorithm to obtain the HF ground state is standard and can be found, for instance, in Ref. 20…”

Section: B Numerical Approachesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

2011

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“…When the field is switched off completely and correspondingly the factor exp(−ν 2 2 /2) omitted from the trial function (4.1) (such that the normalization constant reduces to N 2 = (2Z ) 3 2 +γ / 4πΓ(3 + 2γ) ), the energy functional is given by…”

Section: Stability Of Antibinding For Modified Trial Functionsmentioning

confidence: 99%

“…In accord with the experimental spectrum the electron mass is thereby set equal to zero [1]. Also a mathematical analysis of the two-dimensional confinement by this magnetic field was provided for the case of interacting massless multi-fermions [3].…”

Section: Introductionmentioning

confidence: 99%

Antibinding of atomic electrons in strong inhomogeneous magnetic fields

Jakubaßa-Amundsen¹

2011

Phys. Rev. A

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Abstract. The ground-state energy of heavy one-electron ions in an inhomogeneous locally bounded magnetic field is estimated by the variational principle. The ions are described by means of the pseudorelativistic Herbst/Chandrasekhar operator. Two classes of magnetic fields are considered which model a field-free region around the central charge. It is shown that for a certain size of this region the ground-state energy becomes positive and increases strongly with the magnetic field strength. This behaviour is in contrast to the two-dimensional case where electrons can be bound by such a field-free region.

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“…In Sec. 5, we turn to a waveguide geometry, defined by a suitable inhomogeneous magnetic field [25,26,27,28,29,30,31,32,33,34]. We show that the SOIs give rise to inter-esting spin textures of the chiral states propagating in the waveguides.…”

Section: Introductionmentioning

confidence: 99%

Landau Levels and Edge States in Graphene with Strong Spin-Orbit Coupling

Martino

Hütten

Egger

2013

NATO Science for Peace and Security Series B: Physics and Biophysics

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract We investigate the electronic properties of graphene in a magnetic and a strain-induced pseudo-magnetic field in the presence of strong spin-orbit interactions (SOI). For a homogeneous field we provide analytical results for the Landau level eigenstates for arbitrary intrinsic and Rashba SOI, including also the effect of a Zeeman field. We then study the edge states in a semi-infinite geometry in the absence of the Rashba term. We find that, for a critical value of the magnetic field, a quantum phase transition occurs, which separates two phases both with spin-filtered helical edge states but with opposite direction of the spin current. Finally,we discuss magnetic waveguides with inhomogeneous field profiles that allow for chiral snake orbits. Such waveguides are practically immune to disorder-induced backscattering, and the SOI provides non-trivial spin texture to these modes. Permanent

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Multiparticle equations for interacting Dirac fermions in magnetically confined graphene quantum dots

Cited by 15 publications

References 33 publications

Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

Antibinding of atomic electrons in strong inhomogeneous magnetic fields

Landau Levels and Edge States in Graphene with Strong Spin-Orbit Coupling

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