Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

Journal Article · Tue Feb 15 00:00:00 EST 2011 · Physical Review. B, Condensed Matter and Materials Physics

DOI:https://doi.org/10.1103/PHYSREVB.83.085409· OSTI ID:21538132

Paananen, Tomi; Egger, Reinhold ^[1]; Siedentop, Heinz ^[2]

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1. Institut fuer Theoretische Physik, Heinrich-Heine-Universitaet, D-40225 Duesseldorf (Germany)
2. Mathematisches Institut, Ludwigs-Maximilians-Universitaet Muenchen, D-80333 Muenchen (Germany)

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 {alpha} from the Hartree-Fock approximation and, alternatively, by employing the Mueller 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 {alpha} < or approx. 2, but the Mueller functional leads to an unphysical instability when {alpha} > or approx. 0.756. Up to 20 particles were studied using Hartree-Fock calculations. Wigner molecule formation was observed for strong but realistic interactions, accompanied by a rich peak structure in the addition energy spectrum.

• OSTI ID: 21538132
• Journal Information: Physical Review. B, Condensed Matter and Materials Physics, Vol. 83, Issue 8; Other Information: DOI: 10.1103/PhysRevB.83.085409; (c) 2011 American Institute of Physics; ISSN 1098-0121
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
77 NANOSCIENCE AND NANOTECHNOLOGY
CARBON
COMPARATIVE EVALUATIONS
ENERGY SPECTRA
FERMIONS
HARTREE-FOCK METHOD
HONEYCOMB STRUCTURES
INSTABILITY
INTERACTION RANGE
INTERACTIONS
LAYERS
MAGNETIC CONFINEMENT
MASS
MOLECULES
QUANTUM DOTS
SURFACES
TOPOLOGY
TWO-DIMENSIONAL CALCULATIONS
APPROXIMATIONS
CALCULATION METHODS
CONFINEMENT
DISTANCE
ELEMENTS
EVALUATION
MATHEMATICS
MECHANICAL STRUCTURES
NANOSTRUCTURES
NONMETALS
PLASMA CONFINEMENT
SPECTRA