Physics of new materials: from carbon nanotubes to topological insulators
Abstract:
One of the most stunning discoveries of the last decade is graphene. Apart of being an interesting realisation of a purely 2D crystal, it has extraordinary physical properties. For instance, looking at the electrons in graphene one can learn a lot about the relativistic physics. The reason for this and a large number of different other surprising facts is the special band structure of graphene. In recent years it was realised that graphene is, in fact, one representative member of a completely new class of materials dubbed topological insulators, which are sometimes even called new phase of matter. It turns out that using them one can construct devices, in which one can encounter particles, which are their own antiparticles, aka Majorana fermions, or particles with fractional charges, which are neither bosons, nor fermions (but anyons), or allow for a design of structures, in which one even could encounter the elusive axions. This all not only has given birth to many new research directions but also has helped to improve our understanding of the quantum field theory.
These lectures are intended to give a pedestrian introduction into this fascinating area of research. We shall discuss not only graphene and topological insulators but also understand their connections to Dirac and Weyl semimetals and integer as well as fractional quantum Hall effect and even topological superconductors. Furthermore, we shall try to understand how these materials could be used to generate a whole zoo of exotic quasiparticles. And as an added value we shall definitely take scare out of the concept of band structure and learn a lot of other useful things.