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A class of solutions for the graphene hamiltonian operator

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dc.contributor.authorConca, C.
dc.contributor.authorSan Martín, J.
dc.contributor.authorSolano, Viviana
dc.date.accessioned2024-01-05T12:54:53Z
dc.date.available2024-01-05T12:54:53Z
dc.date.issued2022
dc.descriptionArtículo
dc.description.abstractThe graphene is a substance with carbon atoms arranged in a honeycomb lattice. The dynamics of the electrons in the structure is governed by the Hamilton equations of the system in the form of its associated spectral problem: HΨ = λΨ, with the additional condition that the eigenfunction Ψ must satisfy the so-called Kirchhoff’s conditions. In this paper, we study a class of solutions (λ, Ψ) that, in addition to meeting these conditions, are periodic in one of the two main directions of the lattice, and satisfy a pseudo-periodicity type like condition in the other direction. Our main results lead to an adequate characterization of the dispersion relationships of the honeycomb lattice, providing a precise description of the regions of stability and instability of the eigenfunctions in terms of λ. As a consequence, a tool is thus obtained for a better understanding of the propagation properties and the behavior of the wave function of electrons in a hexagonal lattice, a key issue in graphene-based technologies.
dc.description.versionVersión publicada
dc.format.extent19 p.
dc.identifier.citationMATH. REPORTS 24(74), 1-2 (2022), 139–157
dc.identifier.urihttps://repositorio.udd.cl/handle/11447/8270
dc.language.isoes
dc.subjectPeriodic solutions
dc.subjectStability
dc.subjectGeneral spectral theory
dc.subjectSpectral theory
dc.subjectEigenvalue problems
dc.subjectGraphene
dc.subjectHoneycomb structure
dc.titleA class of solutions for the graphene hamiltonian operator
dc.typeArticle
dcterms.abstractAcceso abierto
dcterms.sourceMATHEMATICAL REPORTS
dspace.entity.typePublication

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