Global well-posedness in a Hartree-Fock model for graphene

TL;DR

This paper proves the global well-posedness of a Hartree-Fock model describing the time evolution of graphene's electrons under external electric potentials, using a non-perturbative quantum electrodynamics framework.

Contribution

It establishes a rigorous mathematical foundation for the dynamics of graphene in the Hartree-Fock approximation, considering external time-dependent electric fields.

Findings

Proved global well-posedness of the model

Applicable to external electric potentials in graphene

Extended non-perturbative QED methods to 2D materials

Abstract

Graphene is a monolayer graphitic film in which electrons behave like two-dimensional Dirac fermions without mass. Its study has attracted a wide interest in the domain of condensed matter physics. In particular, it represents an ideal system to test the comprehension of 2D massless relativistic particles in a laboratory, the Fermi velocity being 300 times smaller than the speed of light. In this work, we present a global well-posedness result for graphene in the Hartree- Fock approximation. The model allows to describe the time evolution of graphene in the presence of external time-dependent electric potentials, such as those induced by local charge defects in the monolayer of carbon atoms. Our approach is based on a well established non-perturbative framework originating from the study of three-dimensional quantum electrodynamics.