PHYS 90507 Topology and Dirac fermions in Condensed Matter

Syllabus PHYS90507 (This is a new course. Comments and suggestions on the content are welcome)

Lectures 1 and 2: Dirac and Weyl fermions. Notes for Lectures 1 and 2

Assignment Set 1Note on assignment 1 about the effective mass.

Lecture 3. The Jackiw-Rebbi solution in 1D. Notes for Lecture 3

Lecture 4. The Jackiw-Rebbi problem in 2D. Notes for Lecture 4

Lectures 5 and 6. The Su-Shrieffer -Heeger model. Notes for Lectures 5 and 6

Assignment Set 2

Lectures 7 and 8. Graphene: band structure. Notes for Lectures 7 and 8

Lecture 9. Graphene: Landau levels. Notes for Lecture 9

Lecture 10. The Berry phase. Notes for Lecture 10

Assignment Set 3

Lecture 11. The Berry phase and the quantum Hall effect. Notes for Lecture 11

Lectures 12 and 13. The Haldane Model. Notes for Lectures 12 and 13

Lecture 14. The Kane-Mele Model.

Lecture 15. Introduction to k.p theory. Notes for Lecture 15

Lecture 16. Review. Presentation

Lecture 17. k.p in III-V and II-VI semiconductors. Presentation

Assignment Set 4

Lecture 18. Dirac bound state at trivial-topological interface. Presentation

Lecture 19. Discussion on spin-charge experimental probes.

Lecture 20 and 21. Topological insulator quantum wells. Notes for lecture 20

Lecture 22. Potential of QAHE for data storage applications. Presentation

Assignment 5

Lecture 23. Symmetry and band crossings. Presentation.

Lecture 24. Transport experiments. Notes for lecture 24

Lecture 25. Optical experiments and photoemission. Notes for lecture 25

Assignment 6