Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2010-11-03
Phys. Rev. B 83, 085409 (2011)
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
8 pages, 8 figures
Scientific paper
10.1103/PhysRevB.83.085409
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 M\"uller 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 $\alpha\alt 2$, but the M\"uller functional leads to an unphysical instability when $\alpha\agt 0.756$. 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.
Egger Reinhold
Paananen Tomi
Siedentop Heinz
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