The discovery of graphene, a one-atom thick layer of carbon atoms forming a honeycomb lattice, represents one of the most outstanding recent achievements in Physics, ackno wledged in 2010 with the Nobel Prize awarded to A. Geim and K. Novoselov. Indeed this material exhibits fascinating properties that make it unique for fundamental physics issues, and that have opened a new era in nanoelectronics. On the one hand, electrons in graphene effectively behave as massless quantum particles in the relativistic regime, opening up the possibility to observe relativistic effects in condensed matter physics, such as the Klein tunneling or the unconventional quantum Hall effect. On the other hand, graphene is characterized by a high carrier mobility and concentration, as well as by extraordinary mechanical flexibility, which make it an ideal candidate as a platform for the foldable electronics in the near future. The purpose of this course is to provide an overview of the electronic properties of graphene, pointing out the peculiarities with respect to conventional materials and their possible application impact. After an introductory part, I shall present the models that are utilized to describe the electronic band structure and the electron transport in bulk graphene and in nanoribbons. In particular, I shall explain why Dirac relativistic quantum mechanics is suitable to describe the electron dynamics in graphene. The second part of the course will be devoted to more specific topics (depending also on the students’ interest), such as Klein tunneling, graphene-based n-p junctions and Veselago lenses, quantum Hall effect in graphene and graphene bilayers.

Basic physics knowledge and linear algebra are mandatory prerequisites. Some basic knowledge of Solid state Physics and Quantum Mechanics is helpful, although not strictly needed (the first part will be devoted to a quick overview of the main concepts)

-Introduction to carbon-based materials -Graphene: overview and general properties -A short survey of electronic properties in solids -The electronic band structure of graphene: from the tight-binding model to the Dirac equation for massless electrons -Relativistic effects in condensed matter: Klein paradox and unconventional Quantum Hall effect -Graphene n-p junctions: Electron focussing and Veselago lenses -Graphene bilayers and tunable band gap

A distanza in modalità sincrona

Presentazione orale

P.D.1-1 - Febbraio