Teaching Physics
Research and teaching go hand in hand. Everyone in the group teaches, postdocs and Ph.D. students included, contributing to the Department's physics curriculum, from first-year exercise classes to specialized Master's-level lectures. Of particular importance are three regular lecture courses that we are regularly involved in teaching.
Introduction to Solid State Physics (402-0255-00L)
Solid state physics is, in truth, the "queen" of the physical sciences. It is supremely practical: the first transistor of 1947 grew into the billions-strong chips in every phone. It may well save the world: superconducting quantum processors are built of Josephson junctions, and every wind turbine turns on rare-earth magnets. It is profoundly fundamental: magnetic monopoles, Dirac fermions, and Majorana states, exotica that particle physicists can only dream of, appear in crystals as collective excitations. And it is fiendishly difficult: a solid is 1023 coupled Schrödinger equations in which the electrons' interaction energy is comparable to their kinetic energy, and their de Broglie wavelength to the distance between atoms, so nothing can be neglected. What a time to join, though: with today's breakthrough materials, with experimental techniques that were state of the art yesterday and are routinely available at user facilities today, and with ever more powerful numerical methods, we finally have the tools to meet the challenge.
This introductory course is a first tour of the whole realm. All the miraculous properties of solids can be traced to one thing: the periodicity of crystals. That is where we begin, with crystal structures and the diffraction experiments that reveal them. We then bring the lattice to life with phonons and the thermodynamics they carry. From there we turn to metals: the free-electron gas, the electronic band structure, and transport. Semiconductors follow, intrinsic and doped, and with them the physics behind the transistor. We conclude with magnetism, of metals and of insulators, the bridge to the quantum many-body physics of the more advanced courses.
The practicalities: a core course of the Physics Bachelor's curriculum worth 8 ECTS credits, taught in English, with three hours of lectures and two of exercise classes each week. The grade is decided at a three-hour written session examination, and yes, a hand-written formula collection is allowed.
Advanced Solid State Physics (402-0257-00L)
A solid is a rather special many-body problem. There are some 1023 particles to deal with. Quantum effects are strong: the de Broglie wavelength of a conduction electron is comparable to the interatomic distance. Interactions are strong as well: the Coulomb repulsion between two neighboring electrons is several electron-volts, the very same scale as their kinetic energy. Nothing is small, and nothing can be treated as a perturbation. The result is the overriding theme of this course: collective quantum phenomena in solids, where enormous numbers of particles act together to produce behavior that none of them is capable of alone.
The course is built in three parts. The first is a self-contained introduction to phase transitions, criticality, and scaling: order parameters and symmetry breaking, Mean Field and Landau theories, and the modern concepts of critical exponents, universality, and topological (Berezinskii-Kosterlitz-Thouless) transitions, with a first look at quantum criticality. The second part sets sail on the "stormy Fermi seas": the susceptibility of the metallic electron gas, charge and spin density waves, metals in high magnetic fields with Landau quantization, quantum oscillations, and the quantum Hall effect, and finally superconductivity, from the London equations to the Josephson effects and BCS theory. The third part turns to the magnetism of insulators: spin Hamiltonians, magnetic structures, spin waves, quantum antiferromagnets, and frustrated magnets.
For all the "theory" in it, this is an experimentalist's course. Every concept is illustrated with experiments, classic and modern, and with actual measured data. Along the way we review the techniques that produce such data today: angle-resolved photoemission (ARPES), resonant X-ray scattering, neutron diffraction and spectroscopy, muon spin rotation, NMR, and others.
The practicalities: a Master's-level course worth 10 ECTS credits, taught in English every autumn semester, with three hours of lectures and two of exercise classes each week. Along the way, every student presents one original research paper to their exercise class; the grade itself is decided at a 30-minute oral exam.
Quantum Solid State Magnetism (402-0532-00L)
Magnetic phenomena are ubiquitous: little magnets on the refrigerator, electric motors, compass needles, MRI machines. They seem so ordinary that we seldom notice the scandal behind them: familiar classical physics is entirely incapable of explaining the workings of the familiar bar magnet, which is no less a quantum object than the superconductor levitating above it. Semi-classical theories in the spirit of Curie and Néel do take us remarkably far, all the way to the "skyrmion" textures of topological magnets. In many materials, however, the microscopic moments stop acting as classical vectors and reveal their true quantum nature. The result is collective many-body ground states and excitations that cannot even be described, let alone understood, in semi-classical terms. Instead, we find analogs of quarks, Higgs bosons, Majorana fermions, and other exotica of high-energy physics. The beauty and attraction of this field is that sophisticated, analytically treatable models find almost exact realization in real, often chemically simple, materials.
The language of this course, throughout, is that of generalized susceptibilities and correlation functions: the most fundamental and universal tools for characterizing the ground state and the hierarchy of excitations in any many-body system, and precisely what modern experiments, from neutron spectroscopy and magnetic resonance to muon spin rotation and resonant X-ray scattering, actually measure. The first semester lays the foundations: linear response, magnetism of metals, the single magnetic ion in a crystal, and magnetically ordered insulators. The second semester starts with magnetic excitations and magnetic phase transitions, and only then climbs into genuinely quantum territory: quantum paramagnets, one-dimensional quantum magnets, and magnetic frustration. Theoretical derivations are balanced by experimental case studies, a mix of classic data of historic value and very recent results.
The practicalities: a course for Master's and doctoral students, taught in English in two semester-long installments. Each has two hours of lectures and one of exercise classes per week, is worth 6 ECTS credits, and is concluded by a 30-minute oral exam.