Embedded Files
Lecture1.pdf- Introduction
- Modeling of solids
- Second quantization
Lecture2.pdf- One-band effective models
- The Hubbard model
- Mean-field Hartree-Fock analysis
Lecture3.pdf- The Heisenberg model
- Spontaneous symmetry breaking
- Holstein-Primakoff representation and spin wave theory
Lecture4.pdf- Superfluidity
- Bose-Einstein condensation
- Interacting superfluids: symmetry breaking
- Bugoliubov excitation spectrum and XY effective action
- Landau's argument and the critical velocity
- Quantization of vorticity in superfluids
Lecture5.pdf- Superconductors as charged superfluids
- The Meissner effect and the London equation
- The Anderson-Higgs mechanism
Lecture6.pdf- BCS theory of superconductivity
- Ginzburg-Landau theory: microscopic derivation
Lecture7.pdf- Ginzburg-Landau theory
- Ginzburg criterion
- Type I and type II superconductors
- Upper critical field
- Flux quantization and the Abrikosov lattice
Lecture8.pdf- The Berezinskii-Kosterlitz-Thouless transition
- Two-dimensional superfluids and superconductors
- The XY model
- Mapping to the Coulomb gas problem
- Mapping to the Sine-Gordon problem
- Renormalization group analysis
Lecture9.pdf- Josephson relation
- Resistance due to vortex motion
- Transport near the BKT transition
Lecture10.pdf- Phenomenology of the quantum Hall effect
- Landau levels
- Quantization of the Hall response of a Landau level
- Edge states
- Effects of disorder
Lecture11.pdf- Quantization of the Hall conductivity
- The Thouless, Kohomoto, Nightingale and den Nijs (TKNN) formula for the Hall conductivity in terms of the Chern number
- Anomalous quantum Hall effect and topological insulators
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