Wigner localization in a graphene quantum dot with a mass gap

TL;DR

This paper demonstrates that massive Dirac electrons in a graphene quantum dot can exhibit Wigner localization, with observable signatures in Coulomb blockade spectroscopy, challenging the notion that graphene's electrons behave as noninteracting.

Contribution

The study provides the first theoretical evidence of Wigner localization in gapped graphene quantum dots using exact diagonalization, accounting for all electron correlations.

Findings

Wigner localization occurs in gapped graphene quantum dots at realistic parameters.

Suppression of fourfold periodicity in filling sequence observed.

Excitation energies are quenched, indicating strong electron correlations.

Abstract

In spite of unscreened Coulomb interactions close to charge neutrality, relativistic massless electrons in graphene allegedly behave as noninteracting particles. A clue to this paradox is that both interaction and kinetic energies scale with particle density in the same way. In contrast, in a dilute gas of nonrelativistic electrons the different scaling drives the transition to Wigner crystal. Here we show that Dirac electrons in a graphene quantum dot with a mass gap localize \`a la Wigner for realistic values of device parameters. Our theoretical evidence relies on many-body observables obtained through the exact diagonalization of the interacting Hamiltonian, which allows us to take all electron correlations into account. We predict that the experimental signatures of Wigner localization are the suppression of the fourfold periodicity of the filling sequence and the quenching of excitation energies, which may be both accessed through Coulomb blockade spectroscopy. Our findings are relevant to other carbon-based nanostructures exhibiting a mass gap.