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arXiv · 2602.19185

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

Louis Garrigue
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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.

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Louis Garrigue. 2026-02-22. Some effective operators for graphene monolayer superlattices, from variational perturbation theory. https://arxiv.org/abs/2602.19185

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