Questions which may guide you to control your understanding

Disclaimer: The following list is an offer - ii is not meant to be comlpete and you better do your own list of relevant topics and interesting questions to be answered!

Elastic properties

• What are stress and strain and how are they linked?
• Which suppositions we usually apply in elasticity theory?
• What is shear stress?
• How many independent component does the elasticity tensor have? Why this number is reduced with respect to "81" and why it depends on the actual system under study?
• How to measure sound velocities? Why there is more than one of them?
• What to learn from the sound velocity experiments on the microscopic properties of a material?

Phonons:

• What is a phonon?
• Why a phonon is considered a quasi-particle?
• How to experimentally determine the phonon dispersion of a material?
• Write energy and momentum conservation laws for an inelastic neutron scattering experiment
• How many phonons can be excited in a material? Is there a way to measure this number?
• What is an acoustic branch?
• Is there always an optical branch? Why?
• Why restricting to the 1st BZ is sufficient?
• Btw, what is the BZ?
• How fast do acoustic wave propagate at q=0, q=pi/a?
• How many branches do you expect for a system with 5 atoms per unit cell?
• Are in general longitudinal or transversal sound waves faster?
• Sketch a typical phonon branch and discuss it
• Can one excite phonons with optical light? Why? Why not?
• Explain Raman scattering
• Explain Brillouin scattering

Thermal Properties

• What is the density of states?
• ... and why is it so important?
• How to calculate the DOS of a given material?
• Does DOS depend on the dimension of a system?
• How to calculate in inner energy U of a lattice?
• What do we learn from measurements of the heat capacity of a material?
• How to measure the heat capacity of a solid?
• Why a material usually expands upon heating?
• How large is the thermal expansion in the harmonic approximation?
• What do we learn by comparing heat capacity (= how the solid stores inner energy) and thermal expansion?
• How to measure the pressure effect on phonons?
• What is the general equation describing heat transport?
• How does the thermal conductivity of a dielectric solid depend on the temnperture? Explain the microscopic effects leading to its characteristic shape.
• How to measure heat transport? Explain two methods - one applicable to nanosized solids or 2D semiconductors.
• What is Matthiessen's rule?
• What is special about the heat transport of a 1D dielectric at low temperatures?

(Mainly on simple) Metals

• Explain the free electron gas model? Which assumption are made, which Ansatz is used, what as the main results?
• On which idea the Sommerfeld approximation is based on?
• Explain and derive the specific heat of the free electron gas. 
• Why different metals have so different Sommerfeld parameters?
• Explain the magnetic response of the free electron gas!
• What is the chemical potential and is it independent on temperature?
• Why iron is ferromagnetic? Explain the underlying microscopic physical mechanis, derive the Stoner criterion and explain it.
• What is a Stoner enhanced paramagnet?
• Explain the response of metal electron on electric fields in the free electron gas model. Why does the fermi sphere start to move in k-space (what does this mean?) and how does nature stop its motion?
• Explain Ohm's law and the Drude equation. 
• What is the Boltzmann transport equation and which terms does it inlcude?
• What is the relaxation time Ansatz?
• Sketch the T-dependence of a metal's resistivity and eplain the relevant physical processes
• Why electron-electron scattering is usually not a prominent factor for resistivity?
• What is special about resistivity in a 1D metal (at low temperatures)?
• What is the Wiedeman-Franz-law and why it is sometimes fulfilled and sometimes not?
• What is a solid electrolyte and why it is important?
• What is Fick's law?
• Which processes are relevant for ionic conductivity?
• How to describe and how to measure ionic diffusion?

Band structure:

• Which are the electronic eigenfunctions in a periodic potential?
• What does "eigenfuntion" imply?
• Explain the empty lattice model and its implications! (PEP5)
• Explain why gaps are formed in the weak potential model (PEP5)
• What are the starting points, suppositions and results in the tight-binding model (or: explain the tight-binding model)
• Explain how the organisation of atoms in a solid results in band formation in the thight-binding model. Argue with physical principles!
• What are the differences and what are similarities between tight-bining and weak lattice models?
• What means "topology"?
• What is a topological insulator and a topological semimetal?
• Why, from a general point of view, twisted layers of e.g. graphen might result in "new physics"?
• How to experimentally determine the band structure of a metal?
• What is the Peierls instability?
• Explain the phrase: "the Fermi surface is instable against a characteristic structural distortion"
• What is the Kohn anomaly?
• How dooes a STM Scanning Tunneling Microscop work in principle?
• Explain the Sommerfeld vs. Bloch scenarios for electrons in a solid.
• ...