Current research in condensed-matter physics is in a significant part concerned with materials where low-energy electronic excitations behave like relativistic elementary particles. These materials thus allow to study intriguing fundamental problems of relativistic quantum mechanics in highly controllable environments on the ``tabletop’’. At the same time, the relativistic behaviour manifests itself in novel transport phenomena, with high potential forfuture applications.
In this course we will introduce/recapitulate relevant aspects of relativistic quantum mechanics (Dirac and Weyl fermions, coupling to the electromagnetic field) and explore some of the associated peculiarities, such as the chiral anomaly. We will then consider simple condensed-matter models of existing materials, with the focus on Weyl semimetals, and explore how and why relativistic particles emerge in matter and what protects them. Afterwards we will study the peculiar consequences and signatures of the relativistic behaviour in materials, especially transport phenomena associated with the chiral anomaly and the charge-conjugation symmetry of relativistic particles, which will bring us to the frontier of current research.
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