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

Lecture notes for Part 1 will be uploaded to https://www.qpec.t.u-tokyo.ac.jp/***** The***** The lecture will be held in-person only, in room 64 on the second floor (2F) of Building 6, School of Engineering. The details of the schedule (lecture days) will be announced on the first day of the lecture (October 2)

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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前提となる知識と項目：Quantum Mechanics Statistical Mechanics / Thermodynamics Solid State Physics 1-3

Profs. Hirschberger and Gong are leading research groups focusing on the topics discussed in this lecture.