Research paperTheoreticalComputational MultiscaleBand StructureSome Effective Operators for Graphene Monolayer Superlattices, from Variational Perturbation TheoryLouis GarriguearXiv·2026·arXiv:2602.19185AbstractOur 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 ε−1 ∈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.Read more
Two-scale graphene monolayer superlattice model with microscopic honeycomb-periodic lattice potential v and macroscopic periodic potentials V and A.1 characterization1 figureSimulatedCStudied Materialperiodic lattice potentialStudied Materialmacroscopic periodic potentialStudied Materialvector potentialStudied MaterialsuperlatticeStudied MaterialExpand
Research paperTheoreticalComputational MultiscaleBand StructureSome Effective Operators for Graphene Monolayer Superlattices, from Variational Perturbation TheoryLouis GarriguearXiv·2026·arXiv:2602.19185AbstractOur 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 ε−1 ∈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.Read more
Two-scale graphene monolayer superlattice model with microscopic honeycomb-periodic lattice potential v and macroscopic periodic potentials V and A.1 characterization1 figureSimulatedCStudied Materialperiodic lattice potentialStudied Materialmacroscopic periodic potentialStudied Materialvector potentialStudied MaterialsuperlatticeStudied MaterialExpand
Research paperTheoreticalComputational MultiscaleBand StructureSome Effective Operators for Graphene Monolayer Superlattices, from Variational Perturbation TheoryLouis GarriguearXiv·2026·arXiv:2602.19185AbstractOur 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 ε−1 ∈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.Read more
Two-scale graphene monolayer superlattice model with microscopic honeycomb-periodic lattice potential v and macroscopic periodic potentials V and A.1 characterization1 figureSimulatedCStudied Materialperiodic lattice potentialStudied Materialmacroscopic periodic potentialStudied Materialvector potentialStudied MaterialsuperlatticeStudied MaterialExpand
Research paperTheoreticalComputational MultiscaleBand StructureSome Effective Operators for Graphene Monolayer Superlattices, from Variational Perturbation TheoryLouis GarriguearXiv·2026·arXiv:2602.19185AbstractOur 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 ε−1 ∈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.Read more
Two-scale graphene monolayer superlattice model with microscopic honeycomb-periodic lattice potential v and macroscopic periodic potentials V and A.1 characterization1 figureSimulatedCStudied Materialperiodic lattice potentialStudied Materialmacroscopic periodic potentialStudied Materialvector potentialStudied MaterialsuperlatticeStudied MaterialExpand