Condensed Matter Physics II (2024)

Syllabus

Topological phases of matter have been one of the most actively studied condensed matter systems in past decades. In this course, we learn the basics of topological insulators and superconductors from the prototypical models to the general classification based on fundamental symmetry.

Contents

  1. [Oct. 8th] Introduction and overview
  2. [Oct. 15th] Review of band theory, Su-Schrieffer-Heeger model, Zero modes
    [numerical diagonalization of the Su-Schrieffer-Heeger model (nb/pdf); exact solution to the Su-Schrieffer-Heeger model with open boundaries (pdf)]
  3. [Oct. 22nd] Chiral symmetry, Winding number, Bulk-boundary correspondence
  4. [Oct. 29th] Topological classification in class AIII, Berry phase
    [Aharonov-Bohm effect (pdf)]
  5. [Nov. 5th] Berry curvature, Chern number
    [Berry phase of a two-level system (pdf)]
  6. [Nov. 12th] Wannier function and polarization (pdf), Laughlin's argument (Thouless pump)
  7. [Nov. 19th] Chern insulator, Dirac model, Chiral edge state
    [numerical diagonalization of the Qi-Wu-Zhang model (nb/pdf); Berry phase of a two-level system (pdf)]
  8. [Dec. 3rd] Z topological invariants (slides), Altland-Zirnbauer symmetry (time-reversal symmetry)
  9. [Dec. 10th] No lecture (due to ISSP workshop)
  10. [Dec. 17th] Altland-Zirnbauer symmetry (particle-hole symmetry), Kramers degeneracy, Symmetry and Berry phase
  11. [Dec. 24th] Z2 topological insulator (Kane-Mele and Bernevig-Hughes-Zhang models), Helical edge state
    [numerical diagonalization of the (generalized) Bernevig-Hughes-Zhang model (nb/pdf); symmetry of the (generalized) Bernevig-Hughes-Zhang model (pdf)]
  12. [Jan. 7th] Fu-Kane Z2 topological invariant (pdf), 1D Z2 topological superconductor (class DIII), 3D Z2 topological insulator (class AII)
  13. [Jan. 14th] Axion electrodynamics, Z2 topological invariants (slides), Classification and dimensional hierarchy (boundary)
  14. [Jan. 21st] Classification and dimensional hierarchy (bulk)
    [Classifying space and Clifford algebra (pdf)]

Reports

References

[Textbooks]

[Reviews]

[Others]