Multiparticle equations for interacting Dirac Fermions in graphene nanostructures
R. Egger, A. De Martino, H. Siedentop, E. Stockmeyer
TL;DR
This paper investigates the energy and stability of interacting Dirac fermions in graphene nanostructures under magnetic confinement using the Hartree-Fock approximation, establishing existence of minimizers and stability conditions.
Contribution
It introduces a mathematical framework for analyzing many-particle interactions in graphene quantum dots with magnetic confinement, including existence and stability results.
Findings
Existence of a minimizer for the energy functional
Derived stability conditions for N-particle systems
Analyzed the effects of Coulomb interactions in confined graphene
Abstract
We study the energy of quasi-particles in graphene within the Hartree-Fock approximation. The quasi-particles are confined via an inhomogeneous magnetic field and interact via the Coulomb potential. We show that the associated functional has a minimizer and determine the stability conditions for the N-particle problem in such a graphene quantum dot.
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