Topological and geometrical aspects of band theory

  title={Topological and geometrical aspects of band theory},
  author={J Cayssol and J N Fuchs},
  journal={Journal of Physics: Materials},
This paper provides a pedagogical introduction to recent developments in geometrical and topological band theory following the discovery of graphene and topological insulators. Amusingly, many of these developments have a connection to contributions in high-energy physics by Dirac. The review starts by a presentation of the Dirac magnetic monopole, goes on with the Berry phase in a two-level system and the geometrical/topological band theory for Bloch electrons in crystals. Next, specific… 

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