Concepts in Materials Physics

This course is an introduction to the quantum mechanics of functional materials. We will cover fundamental concepts such as phonons, crystal electrons and other quasi particles which are used to model functional properties of materials such as metals, semi-conductors, magnets, superconductors etc. A profound knowledge of these concepts is essential to pass most compulsory modules of our master's programme. The lecture starts with the very basics such as atomic orbitals, the periodic table and crystal lattices in the first two weeks to get everybody on board. Then we will move on the the quantum mechanical description of lattice vibration, the quantum mechanics of electrons in metals, semiconductors and other quantum related phenomena. A word of caution: To our experience, the difficulty to understand quantum mechanics and to apply it to solid state phenomena is often underestimated. If you are not yet fluent with Hamilton operators, second quantization or other qm concepts you will need your time to digest the topic. We thus strongly recommend that you attend the lecture, tutorials and excercises in person. Content • Properties of crystalline solids: orientation dependence, lattice and reciprocal lattice, semiconductors, metals and isolators. • Lattice dynamics: lattice with monatomic and diatomic basis, dispersion relation, Brillouin zones, acoustic and optical modes, phonons, density of states, specific heat, thermal transport, thermal expansion. • Metals: electronic structure, band model, free electron gas, density of states, Fermi-Dirac statistics, Bloch functions • Electronic transport: Drude model, Drude-Sommerfeld model, thermal properties of the electron gas. • Semiconductors: synthesis (examples), doping, electronic transport, effective mass, chemical potential, optical properties, density of states, diodes. • Solid state ionics: ionic and mixed transport. • Dielectric properties: polarisation and polarizability, electronic and ionic polarization, optical properties, electro-elastic properties • Magnetism: para, dia- and ferromagnetism, magnetism of solids.