PHYS 567 :: Physics Illinois :: University of Illinois at Urbana-Champaign

Course Description

Introduction to the role of crystal symmetries and Berry phases in modern condensed matter physics. Topics include group theory and representation theory, space groups and their representations, electric polarization, Wannier functions, topological insulators, the quantum Hall effect, and the theory of band representations.

Credit: 3 graduate hours.

Prerequisite: PHYS 560 or equivalent.

Course Goals

Upon completion of the course students will be able to:

• Understand the foundations of group theory in solid state physics
• Analyze and evaluate research papers on topological materials
• Apply Berry phase techniques to analyze electronic properties of materials

 

Useful Resources

While this course will not follow any single textbook, you may find the following resources useful:

• D. Vanderbilt, Berry Phases in Electronic Structure Theory
• C. Bradley and A. Cracknell, The Mathematical Theory of Symmetry in Solids
• J. P. Serre, Linear Representations of Finite Groups
• M. Dresselhaus, Applications of Group Theory to the Physics of Solids
• J. Avron, Lectures Adiabatic Quantum Transport
• B. Bradlyn and M. Iraola, Lecture notes on Berry phases and topology

Online Space Group Tables and Tools can be found via at the Bilbao Crystallographic Server