授课人：杨栩博士 (Postdoctoral Scholar at the Center for Emergent Materials of The Ohio State University)
I will focus on the role of geometry in condensed matter physics. I will develop necessary mathematical techniques in solving physics-motivated problems along the way. Topics including the Fermi liquid theory, quantum Hall effects, response theories and quasi-crystals will be discussed. Mathematical tools of Morse theory and algebraic topology will be introduced.
This short course will be lectures aiming at providing students with a perspective of the role of geometry in condensed matter physics. Students with a general physics and math background (~level of sophomore) and a certain degree of mathematical maturity are encouraged to enroll.
Morse Theory, J. Milnor
Solid State Physics, N. Ashcroft and D. Mermin
Many-Body Physics, Topology and Geometry, S. Sen and K. Gupta
Geometric Phases in Physics, A. Shapere and F. Wilczek (ed.)
Topology in Condensed Matter, M. I. Monastyrsky (ed.)
I will be focusing on the following topics:
1. Introduction to Morse theory: Morse inequality
2. Physics of van Hove singularities: quantum oscillations, Lifshitz transitions, shape of Fermi surfaces
3. Weyl semimetals and the idea of Berry phases
4. Insulators: crystals, quasi-crystals and topological defects
5. Insulators: band topologies
There will be homework problems to help students get familiar with ideas and calculations. In addition, I would recommend students write a term paper about interesting topics related to geometry in condensed matter physics. I will provide references if students need guidance/advice on the potential topics of their interest.