Juliá-Díaz, BrunoDauphin, AlexandreMiranda Riaza, Marc2022-09-062022-09-062022-06https://hdl.handle.net/2445/188731Treballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2022, Tutors: Bruno Juliá-Díaz, Alexandre DauphinWe study the electronic structure of graphene and the corresponding phases. We first examine the non-interacting part of the Hamiltonian and show the appearance of Dirac cones. Later we study the full Hamiltonian through Mean-Field theory and show a process of symmetry breaking that leads to the formation of a Charge Density Wave (CDW) phase. We show how Automatic Differentiation, a tool from Machine Learning, can be used as an alternative to the Self-Consistent Field method5 p.application/pdfengcc-by-nc-nd (c) Miranda, 2022http://creativecommons.org/licenses/by-nc-nd/3.0/es/GrafèEstructura electrònicaDiagrames de faseTreballs de fi de grauGrapheneElectronic structurePhase diagramsBachelor's thesesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess