PHYS 598GTC :: 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.

Course 4 graduate hours. Prerequisite: PHYS 560 or equivalent.

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