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] Altland-Zirnbauer symmetry (time-reversal symmetry and particle-hole symmetry)
  9. [Dec. 10th] No lecture (due to ISSP workshop)
  10. [Dec. 17th] Kane-Mele and Bernevig-Hughes-Zhang models, Kane-Mele Z2 topological invariant
  11. [Dec. 24th] Fu-Kane Z2 topological invariant, Symmetry indicator
  12. [Jan. 7th] Higher dimensions: dimensional hierarchy (1)
  13. [Jan. 14th] Higher dimensions: dimensional hierarchy (2)
  14. [Jan. 21st] Tenfold classification

Reports

References

[Textbooks]

[Reviews]

[Others]