Artifical atoms in interacting graphene quantum dots
Wolfgang H\"ausler (1, 2), Reinhold Egger (1) ((1) University of, D\"usseldorf, Germany, (2) University of Freiburg, Germany)
TL;DR
This paper develops a theoretical framework for understanding Coulomb-correlated electrons in graphene quantum dots, overcoming divergences in the Dirac spectrum, and presents exact solutions for a two-electron system analogous to an artificial helium atom.
Contribution
It introduces a novel application of Sucher's projection formalism to graphene quantum dots, enabling well-defined solutions for relativistic electron interactions.
Findings
Exact diagonalization results for two-electron graphene quantum dots.
Identification of divergences in naive Dirac spectrum generalizations.
Development of a formalism to handle Coulomb interactions in relativistic graphene systems.
Abstract
We describe the theory of few Coulomb-correlated electrons in a magnetic quantum dot formed in graphene. While the corresponding nonrelativistic (Schr\"odinger) problem is well understood, a naive generalization to graphene's "relativistic" (Dirac-Weyl) spectrum encounters divergencies and is ill-defined. We employ Sucher's projection formalism to overcome these problems. Exact diagonalization results for the two-electron quantum dot, i.e., the artificial helium atom in graphene, are presented.
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