3 ECTS Credits — Semester 2 — Elective
Quantum Matter refers to the peculiar behavior of matter at the quantum scale, where particles exhibit wave-like properties and can exist in multiple states simultaneously. This field of study combines principles from quantum mechanics and condensed matter physics to explore unique phenomena such as superconductivity, quantum magnetism, and topological insulators. The behavior of quantum matter often results in collective properties that cannot be explained by classical physics.
Syllabus
- Quantum oscillators: application to phonons and bosonic collective applications
- Second-Quantization for bosons and fermions.
- Applications to the weakly interacting Bose gas and to quantum magnets.
- Modern Band theory :
- Bloch theorem, Bloch waves, Bravais lattice
- Tight binding models in first and second quantized form
- Beyond the monoatomic crystal : crystal lattices with basis (ex: graphene): Metals, insulators (semiconductors), semimetals, etc. Notion of band mass.
- Symmetries: time-reversal symmetry, particle-hole symmetry, chiral symmetry.
- Dirac materials and Dirac matter: Introduction to topology in Dirac 2-band Hamiltonians such as graphene and its derivatives (Dirac monopole, Berry phases, Chern insulators).
- A first attempt to include interactions to the free electron gas: The Hubbard model and the Mott-insulator transition.
- Some instabilities of the free Fermi gas: BCS theory.
Suggested bibliography
- N. W. Ashcroft, N. D. Mermin, Solid state Physics, Saunders College Publishing.
- D. Vanderbilt, Berry Phases in Electronic Structure Theory, Cambridge University Press.
- P. Coleman, Introduction to many body physics, Cambridge University Press.
Prerequisites
- Introduction to Quantum Solid State Physics
- A good handle on quantum mechanics and statistical physics