Maxim Breitkreiz




Sommer term 2020:

Relativistic Particles in Condensed Matter



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

·       special and general relativity

·       relativistic quantum mechanics

-      Dirac and Weyl fermions, coupling to the electromagnetic field

-      Klein paradox, chiral anomaly

·       tight-binding model of condensed matter


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.


Teaching form

·       Live video conferences (blackboard lecture and discussions) during original lecture appointments Mondays 12:00 – 14:00 starting 20.04.2020

·       Lecture notes with short exercises for self-study

·       Discussion forum


Exam: Presumably online presentation of a recent paper. Alternatively a reproduction of a recent publication as a homework assignment (to be decided).


Literature: Lecture notes, and lit. for further reading will be provided. 

Online Access

Please register for this lecture in Campus-Management.


Vorlesungsnummer 20120401 (Vorlesung) und 20120402 (Übung).

One day after registration, you can access this course via Blackboard


Blackboard is the main platform for this course, where you will find further information and teachig material.


Contact to lecturer

If you have troubles signing in or you have other questions, please write an email to

breitkr at