固体物理第四

Contents (Hirschberger): 1. Introduction: Topological matter: via response to external current 2. Gauge transformation in Quantum Mechanics: electromagnetic field (in ‘first’ quantization) 3. Example A: Aharonov-Bohm effect 4. Example B: Dirac monopole and charge quantization 5. Berry phase: Gauge field beyond electromagnetic vector potential (‘virtual gauge field’, emergent electrodynamics) 6. Example A: Berry phase for two-level system (abstraction of Dirac monopole) 7. Example B: Monopoles in k-space, Chern number of Weyl semimetal 8. Example C: Monopoles in real space: magnetic soliton (skyrmion) 9. Example D: Dynamics of emergent field, emergent inductance 10. Advanced topics: Modern theory of polarization, and orbital magnetization Contents (Gong): -- Equilibrium Part -- 1. Introduction: motivation, quadratic Hamiltonian/Gaussian states, fundamental symmetry (Altland-Zirnbauer) classes 2. Integer quantum Hall effects (IQHE): Hofstadter model, Chern insulators (anomalous IQHE), bulk-edge correspondence 3. Topological insulators (TI): Z_2 time-reversal-symmetric TI, SSH model, periodic table -- Nonequilibrium Part -- 4. Quench in topological phases: dynamical symmetry breaking, spate-time topology, dynamical phase transition 5. Floquet topological phases: adiabatic pump, Floquet engineering, anomalous Floquet TI 6. Dissipative topological phases: Markovian free-fermion systems, non-Hermitian systems 7. Outlook

Students will complete two problem sets which are graded by the professors. One problem set will be a mid-term assignment.

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事前履修：固体物理第一,固体物理第三,固体物理第二