Chern number Gauge invariance Peierls substitution linear response Kubo formula integer quantum Hall effect Berry curvature Chern number TKNN formula Electron Hamiltonian in electromagnetic field ID: 1022651
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1. Week 11,Magnetic field, Haldane Model, Chern number Gauge invariance, Peierls substitution, linear response, Kubo formula, integer quantum Hall effect, Berry curvature, Chern number, TKNN formula
2. Electron Hamiltonian in electromagnetic field
3. Haldane model (1988) AB
4. The Haldane model in k space nearest neighbor vectors denoted by red arrows, next nearest neighbor vectors denoted by grey dotted arrows.
5. Linear response theory for conductivity0
6. Apply Wick’s theorem to compute GJJ
7. Back to real time t and then
8. From contour to retarded
9. DC conductivity, 0
10. Berry phase/Berry curvature 20 1
11. Computing Berry curvature from eigenstates
12. Chern number, TKNN formula (1982)
13. Haldane modelTop left: real space and reciprocal space geometry.Left: band structure at fixed and , as decreases from 0 passing the critical point, when , in (c).Top: Berry curvature for different (as in left figure (a), (b) and (d)).
14. DC conductivity, taking the 0 limit differently
15. Other aspects of Berry phase physicsInterpretation/calculation of electro-polarization of ferroelectric materials Electron-phonon interaction in Born-Oppenheimer approximationElectron transport in adiabatic driven systemsBerry phases in periodic driven systems, Floquet theory, etc