Electronic properties of graphene: A learning path for undergraduate students

The purpose of this work is to present a learning path aimed at deepening student understanding of the fundamental concepts underlying the electronic properties of new materials, graphene in particular. To achieve this task, we propose a five-week long workshop where students may be introduced to fundamental concepts of advanced physics, rarely used in learning paths, such as the symmetry properties of the crystal lattice, the group theory, the features of the free electron wave functions and energy levels, the relativistic Dirac equation. Particular emphasis is given to the manner of introducing these concepts, since an essential knowledge of solid state physics, quantum physics and relativity is first necessary. We here present and discuss these concepts as preliminary steps towards a learning sequence that may guide physics/engineering undergraduates to reach a deeper understanding of the physics underlying the complex world of graphene and its properties. The conceptual framework might support both instructors and students toward further scientific investigations