Magnetic Triplet Excitations in Graphene

When doping graphene an unique window appears in the electron–hole excitation spectrum. Including the Coulomb interaction through the Hubbard Hamiltonian results in bound state formation in graphene. The bound states we analyze represent triplet excitations, i.e. magnons, with spin 1. When increasing the strength of the Coulomb interaction, electron–hole pairs are dragged down into the window. This is a property of the triplet excitations since the interaction term is negative, indicating attraction, in that context. We analyzed further the dispersion relation for U ' 11 eV and at last we investigated the appearance of magnons in real space. Résumé Når man doper grafen opstår der et unikt vindue i elektron–hul eksitation spektret. Inklusionen af Coulomb vekselvirkningen gennem Hubbard Hamiltonianen resulterer i dannelsen af bundne tilstande i grafen. De bundne tilstande der analyseres representerer triplet eksitationer, i.e. magnoner, med spin 1. Forøges styrken af Coulomb vekselvirkningen, bliver elektron–hul parrerne trukket ned i vinduet. Det er en egenskab af triplet eksistationerne eftersom vekselvirknings ledet er negativt, hvilket indikerer tiltrækning i denne kontekst. Yderligere analyserede vi dispersion relationen for U ' 11 eV og til sidst undersøgte vi hvordan magnoner opstår i det reele rum.