Solid State Physics
Introduction and review of quantum mechanics & statistical mechanics.
Crystal lattice: real and reciprocal space lattice, X-ray detection.
Bloch theory: Bloch theorem, Bloch and Wannier basis.
Tight-binding models.
Topology in 1D: SSH chain with chiral symmetry, and its classifications.
Topology in 1D: polarization and the physical meaning of classification.
Topology in 2D: symmetry enforced Dirac points in graphene; Haldane honeycomb model.
Topology in 2D: Chern number and adiabatic charge pumping.
Semi-classical description of electrons' dynamics, anomalous velocity.
Boltzmann equation and relaxation time approximation.
Landau Fermi liquid: concept of quasi-particles and weakly interacting Fermi sea.
Landau Fermi liquid: thermodynamic properties.
Quantum Hall effect: Landau level and wavefunctions.
Quantum Hall effect: topological quantization of the integer quantum Hall conductivity --- gauge invariance and role of disorder.
Quantum Hall effect: fractionalization, anyon and Laughlin wavefunction.
Lecture 16
Quantum Hall effect: quantum oscillation and mapping Fermi sea.
Superconductivity: phenomenology, London equation.
Superconductivity: mean field theory.
Superconductivity: BCS wavefunction and gap equation.
Superconductivity: Majorana fermion and 1D Kitaev chain.
Superconductivity: Majorana vortex mode in 2D p+ip wave superconductivity.
Superconductivity: Ginsburg-Landau Theory and Anderson-Higgs Mechanism
Superconductivity: Josephson effect and quantum applications
Quantum magnetism from non-interacting electrons
Quantum magnetism: direct and super exchange mechanism
Lecture 26
Quantum magnetism: Hubbard model