Introductory course in Quantum Topology in Condensed Matter

In this one-week course, Tomoki Ozawa will discuss basics of topological phases of matter, such as the quantum Hall effect and topological insulators. Topological phases of matter is a growing field of research in various fields of condensed matter physics, and a goal of this course is to understand how the idea of topological phases is applied, in particular, in photonic systems. The plan is to give the first four lectures on a blackboard, and final lecture with a computer presentation. Only a basic knowledge of solid-state physics, such as the Bloch theorem and band structure, is assumed.

The tentative list of topics which will most likely be covered in the five lectures:
1. Introduction to topological concepts (Berry phase, Berry connection, Berry curvature, and Chern number)
2. Integer quantum Hall effect (TKNN formula, Harper-Hofstadter model, bulk-boundary correspondence)
3. Quantum spin Hall insulators (Haldane model, Time-reversal symmetry, Kane-Mele model)
4. Classification of topological phases (ten-fold way, Su-Shrieffer-Heeger model)
5. Topological photonics

Schedule: