STUDY OF ANALYTICAL SOLUTIONS OF THE DIRAC EQUATION IN 3+1 DIMENSIONS WITH CIRCULAR SYMMETRY AND THEIR APPLICATIONS TO BOUND STATES IN GRAPHENE

• Grant number: 24/16575-7
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: January 01, 2025
• End date: May 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Antonio Soares de Castro
• Grantee: Vitor Bentes Mendrot
• Host Institution: Faculdade de Engenharia (FEG). Universidade Estadual Paulista (UNESP). Campus de Guaratinguetá. Guaratinguetá , SP, Brazil

Abstract

The approximation via the tight-binding model to study the excited states around the Dirac points of graphene results in a massless Dirac theory in (2+1)-dimensions. In the literature, there is a plethora of works that use this formulation to study the confinement of fermions in graphene. This research project offers as an alternative the study of graphene with a Dirac theory in (3+1)-dimensions. We are looking for configurations of different couplings and functional forms for potentials with circular symmetry that allow for the confinement of fermions. The implementation of this formulation allows for a wider range of couplings, opening up the possibility of broader options for realizing fermion confinement.