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.

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

Hubbard model at strong coupling: Heisenberg and t-J model