Advanced Condensed Matter Theory



Course Syllabus pdf file

Lecture notes

  • Lecture 1 : Jackiw-Rebbi mode (domain-wall fermions), Su-Schrieffer-Heeger model
    Ref: Heeger, Kivelson, Schrieffer, Su, RMP 60, 781 (1988).
    Jackiw and Rebbi, PRD 13, 3398 (1976).
  • Lecture 2 : Spin model, AKLT, string order, edge mode
  • Lecture 3 : Topological 1D superconductor, Majorana modes, Kitaev chian
  • Lecture 4 : Integer quantum Hall (Landau gauge), Laughlin argument
  • Lecture 5 : Landau level (symmetric gauge), guiding center
  • Supplementary material : U(1) Berry phase
  • Supplementary material : Geometric picture on Berry phase
  • Supplementary material : Non-Abelian Berry phase
  • Lecture 6 : Topological index for quantum hall systems
  • Lecture 7 : Calculate the QHE conductance
  • Lecture 8 : The lattice Hofstadter problem -- Dirac fermions
  • Lecture 9 : Bulk-edge correspondence -- Riemann surfaces, link number
  • Lecture 10 : Honycomb lattice - graphene, valley Hall, quantum anomalous Hall
  • Lecture 11 : Quantum spin Hall, Kane-Mele, Zhang's model


    Howework assignment

    Final project








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    Last modified: Jan 7, 2010.