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.