Some effective operators for graphene monolayer superlattices, from variational perturbation theory

TL;DR

This paper develops precise effective operators for graphene monolayer superlattices using a combination of variational perturbation theory and multiscale methods, replacing the Dirac operator with more accurate models.

Contribution

It introduces a novel approach coupling variational approximation, perturbation theory, and multiscale analysis to derive effective operators for graphene superlattices.

Findings

Effective operators differ from the standard Dirac operator.

Simulations demonstrate the accuracy of the new operators.

The method improves modeling of graphene superlattices.

Abstract

Our goal is to provide precise effective operators for monolayer graphene at Fermi energy. We consider the microscopic potential created by a lattice, and add a macroscopic potential with the same periodicity but varying at a scale $\varepsilon^{-1} \in \mathbb{N}$, creating a superlattice. Our approach consists in coupling the variational approximation, perturbation theory together with a multiscale method. At the effective level the usual massless Dirac operator is replaced by other operators, and we provide simulations in the case of graphene.