Quantum Materials II

Quantum field theoretical methods: Second quantization, field operators, creation and annihilation operators, quantum statistics for Fermions and Bosons. Quantum statistical methods: Formulation of partition function, free energy, internal energy, entropy, specific heat, average occupation numbers for free particles, the dimensionality of the density of particle states. Semi-classical description of Landau Fermi liquid and Boltzmann transport equation. Scattering theory and Landauer transport formalism. Conductance measurements in one- and two-dimensional materials. Tight-binding models. Experiments probing the band structure of quantum materials. Beyond single-particle models, derivation of the Hartree and Hartree-Fock approximations, the introduction of exchange, the introduction of phonons and the derivation of electron-phonon coupling. Superconductivity.