Material de apoio usado no curso de física da matéria condensada de graduação no instituto de física da UFF no segundo semestre de 2019.

Reinaldo de Melo e Souza

Condensed Matter – Marcel Franz

Condensed Matter – Marcel Franz

Lecture 1: Solids as interacting quantum many-body systems, basic Hamiltonian. Born-Oppenheimer approximation.

Lecture 2: Second quantization for fermions and bosons

Lecture 3: Electron gas; jellium model; ground state energy due to interactions.

Lecture 4: Hartree-Fock (mean-field) approximation. Screening: Thomas-Fermi (semiclassical) approximation, Lindhard dielectric function.

Lecture 5: Bose-Einstein condensation; Bogoliubov theory of liquid helium: Hamiltonian, Bogoliubov transformation, energy spectrum

Lecture 6: Lattice vibrations, phonons; Phonon specific heat and the Debye model.

Lecture 7: Magnons, Heisenberg Hamiltonian, Holstein-Primakoff transformation, ferromagnetism.

Lecture 8: Electrons in a periodic potential, Bloch's theorem, the case of weak potential.

Lecture 9: Band structures, metals, insulators. Tight-binding Hamiltonians.

Lecture 10: Transport: Semiclassical theory of electron dynamics, relaxation time approximation.

Lecture 11: Topological phases of matter: examples, band theory,Berry curvature and phase. Polarization and topology.

Lecture 12: Polyacetylene and the Su-Schrieffer-Heeger model; Chern insulator; Energy spectrum of graphene and time-reversal invariance.

Lecture 13: Hamiltonian for graphene and inversion symmetry; Haldane and Semenoff masses. Superconductivity: Cooper pair problem.

Lecture 14: Electron-phonon coupling and attractive interaction; BCS ground state, gap equation and its solution at zero temperature.

Lecture 15: Bogoliubov-deGennes theory of superconductivity; BCS gap at finite temperature; Ginzburg-Landau theory and electromagnetic properties.

Arindam Kumar Chatterjee