Signatures of Wigner molecule formation in interacting Dirac fermion quantum dots

TL;DR

This paper investigates the formation of Wigner molecules in interacting massless Dirac fermions confined in quantum dots, using various computational methods to analyze ground state energies and particle arrangements.

Contribution

It introduces a comparative study of Hartree-Fock and Müller functionals for modeling interacting Dirac fermions in quantum dots, highlighting the conditions for Wigner molecule formation.

Findings

Hartree-Fock provides accurate energies for interaction parameter α < 2

Müller functional shows unphysical instability for α > 0.756

Wigner molecules form at strong interactions, with characteristic spectral peaks

Abstract

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.