Table of Contents

Slides, tutorial sheets and lecture notes are only available for students of the Advanced CMP lecture for personal use as part of their studies. All rights of these materials are reserved. Any commercial use is prohibited.

0. General issues and introduction (slides)

• How to get a certificate
• Tutorials
• What is Condensed Matter Physics?
• What should you have learnt before?
• What may you expect from this lecture?
• Link: Nobel prizes in Physics

1. Elastic properties of solids (slides)

• Formation of solids, chemical bonds (reminder to PEP5)
• Continuum approximation
• Stress tensor
• Strain tensor
• Elasticity tensor
• Young's modulus, bulk modulus, shear modulus, Poisson ratio
• Sound waves in solids
• Nobel prize 1991: de Gennes, liquid crystals etc.

2. Lattice Dynamics (slides)

• Reminder: Phonons (PEP5)
• Reminder: DOS (PEP5)
• Experimental determination of phonon disperion: Inelstatic neutron scattering
• Link: Phonon dispersion database
• Link: Inelastic neutron scattering, ILL, Grenoble
• Link: Noble Prize Physics 1994 (neutron scattering techniques)
• Raman scattering
• Link: Venkata Raman Nobel Prize 1930
• Raman vs. IR spectroscopy
• Brillouin scattering

3. Thermal properties of the crystal lattice (slides)

• Density of states
• Reminder: Heat capacity
• Einstein-Model, Debye-Model
• Heat capacity of 2D materials
• Link: Nobelpreis 1936 Chemie: P. Debye
• Advanced reading: Thermal properties of graphene: Fundamentals and applications (specific heat, heat transport, phonon dispersion of graphene)
• Nobel prize 2010: Graphene
• Thermal expansion
• Advanced reading: Elastic and vibrational internal/free energy: Balcerzac2010
• Grüneisen relation
• Advanced reading: Pressure-Raman effects and vibrational scaling laws in molecular crystals (link)
• Reminder: Phononic heat conductivity
• Matthiessen's rule, phonon-phonon scattering
• Advanced reading: Thermal conducitivity of carbon nanotubes (review on current research results)
• 1D heat transport
• Quantisation of heat conductance
• Link: Schwab et al., Measurement of the quantum of thermal conductance, Nature 2000
• Correction of the formula about the 3ω method and definition of the thermal conductance G₀

4. Simple metals (slides)

• Free electron gas model: short review
• The Sommerfeld approximation: Taylor expansion with fermions
• Specific heat of the free electron gas: Storing energy by conduction electrons
• Pauli-Susceptibility: Magnetism of the free electron gas
• Ferromagnetism, Stoner Model: Why a metal can be a ferromagnet (and what is surprizing about it)?
• Electrical conductivity of metals: motion in k-space!
• Boltzmann transport equation
• Skript: Yes, the lackboard formula is correct + Example of Boltzmann equation
• 1D metals: Quantized electric transport
• Thermal conductivity of metals
• Wiedemann-Franz-law
• 1D metals: Quantized heat transport
• Advanced reading: Quantized thermal transport in single-atom junctions, Science 2017
• Solid state electrolytes: Charge transport in dielectrics!
• Fick's law and Einstein-Nernst equation
• How to measure diffusion coefficients
• Why are solid state electrolytes so important?
• Instead of a textbook: See the literature (100s of papers + books)!
• Example 1: Fundamentals of inorganic solid-state electrolytes for batteries
• Example 2: Unlocking the secrets of ideal fast ion conductors for all-solid-state batteries

5. Electronic band structure (slides)

• Bloch theorem, Bloch electrons
• Link: Felix Bloch: Über die QM der Elektronen in Kristallgittern, 1928
• Nearly free electrons
• Energy gap
• Tight binding model
• Strongly bound electrons, tight binding
• Topological materials: Classification regarding topology
• Link: A new schema to classify materials (via Nature Journal 2020)
• Link: Weyl Metals (Felser et al, Physik Journal 2021)
• Twisted graphene multilayers: Creating a Moiree potential: Efretov, Physik Journal 2021
• PES, ARPES
• Link: ARPES spectrometer at Spring8, Japan
• Link: Intro to ARPES, Shen group at Stanford University
• Nobel prize 1921 (photoeffect) and 1981 (electron spectroscopy)
• Electron-phonon coupling: Peierls transition in 1D metals
• Advanced reading: van Smaalen, The Peierls transition in low-dimensional electronic crystals
• Effective mass, meaning of k
• Heavy fermion systems
• Motion of electrons in E-field
• Advanced reading: 1st exp observation of Bloch osc: Lyssenko 1997

6. Electrons (in solids) in external magnetic field (slides)

• Cyclotron resonance
• Landau levels
• Nobel prize 1962 - Lev Landau
• De Haas-van Alphen effect
• Shubnikov-de Haas effect
• Determining Fermi surface by quantum oscillations
• Quantum Hall Effect(s)
• Nobel prize 1985: Integer QHE Klaus v. Klitzing
• Nobel prize 1998: Fractional Quantum Hall Effect
• Nobel Prize 2016: Topological Phases of Matter: Diect relevance for QHE: see chapter 4 of explanations of the NP2016
• Novoselov et al, Nature 2005
• Nobel prize 2010: Graphene
• Illustrative review paper in Graphene: Materials Today
• Magnetoresistive effect in simple metals
• MR in ferromagnets
• Giant Magnetoresistance (GMR)
• Link Nobel Prize Fert, Grünberg, Royal Swedish Acad. Sc.
• Link: Explanation of GMR@Nobelprize.org
• Magnetic data storage, read/write heads

7. Semiconductors (slides)

• Intrinsic semiconductors; Mass action law of SCs (short reminder)
• Doped SCs, Hydrogen model (short reminder)
• Excitons
• Quantum size effect in semiconducting NPs
• Advanced reading: Excitons in Nanoscaled Systems (Nature 2006)
• SC heterostructures: pn-junction
• Nobel prize 2000: SC hetero structures
• Zener diode
• LED, solar cell
• Nobel Prize 1973: Tunelling diode
• Nobel prize 2014: Blue diodes
• Nobel prize 2009: CCD sensor
• Bipolar transistor: Nobel Prize 1956
• Semiconductor laser
• Schottky contact
• MOSFET; 2DEG

8. Magnetism (slides)

• Diamagnetism
• Paramagnetism, Curie law
• 3d vs 4f magnetism: Crystal fields and Quenching of orbital momentum
• Nobel prize 1977: Anderson, van Vleck, Mott: "many body physics"
• Mean field model and deviations
• Nobel prize 1982: Wilson - phase transitions, critical phenomena
• Curie-Weiss law
• Ferromagnetism, Stoner Model
• Magnons
• Magnetic domains
• Superparamagnetism
• Antiferromagnetism and Ferrimagnetism
• Nobel prize 1970: L. Neel

9. Superconductivity (slides)