Lecture contents

Lecture notes provided below are not a complete script. Please refer to the literature textbooks for a more complete and typo-free presentation of condensed matter physics.

Slides, tutorial sheets and lecture notes are only available for students of the 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 (bare slides)

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

 

1. Elastic properties of solids (bare slides) (slides+notes) (bare notes)

• Formation of solids, chemical bonds (PEP5)
• Link: Definition of crystal both in real and reciprocal space (link)
• 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 (bare slides) (bare notes) (slides+notes)

• Reminder + self test: Phonons (PEP5)
• Reminder: DOS (PEP5)
• Reminder: Experimental determination of phonon dispersion: Inelastic neutron scattering (PEP5)
• 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 (bare slides) (bare notes) (slides+notes)

• Reminder PEP5 Density of states
• Reminder PEP5: 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 PEP5: Phononic heat conductivity
• Matthiessen's rule, phonon-phonon scattering
• 3-omega method: heat transport by voltage measurements
• Advanced reading: 3omaga method (link)
• 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
• Focussing of phonons
• Towards application: Nature 2017: Heat guiding and focusing using ballistic phonon transport in phononic nanostructures (link)
• Towards application: phonon transistors, computing with phonons, phonon waveguides, and cooling solutions for microelectronics

 

4. Simple metals (bare slides, slides with notes, bare notes)

• Free electron gas model: short review
• The Sommerfeld approximation
• Specific heat of the free electron gas
• Pauli-Susceptibility
• Electrical conductivity of metals
• Boltzmann transport equation
• 1D metals: Quantized electric transport
• Advanved Reading: 1d conductor (Damyadov 2015)
• Advanced Reading: Quantized Conductance Atomic Switch, nature 2005
• Thermal conductivity of metals
• Wiedemann-Franz-law
• 1D metals: Quantized heat transport
• Advanced reading: Quantized thermal transport in single-atom junctions, Science 2017

 

5. Electronic band structure (slides, slides with notes, bare notes)

• Bloch theorem, Bloch electrons
• Link: Felix Bloch: Über die QM der Elektronen in Kristallgittern, 1928
• Nearly free electrons
• Energy gap
• Electron-phonon coupling: Peierls transition in 1D metals
• Advanced reading: van Smaalen, The Peierls transition in low-dimensional electronic crystals
• 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 2D materials: 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)
• 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 (bare slides, slides with notes, lecture notes)

• 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 effects: Overview
• Anisotropic Magnetoresistance (AMR)
• Giant Magnetoresistance (GMR)
• Link Animation GMR (FZ Jülich)
• Link Nobel Prize Fert, Grünberg, Royal Swedish Acad. Sc.
• Link: Explanation of GMR@Nobelprize.org
• Tunneling MR (TMR)
• Magnetic data storage, read/write heads

 

 

7. Semiconductors (slides, slides with notes, lecture notes) 

• 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 2014: Blue diodes
• Nobel prize 2009: CCD sensor
• Bipolar transistor
• Semiconductor laser
• Schottky contact
• MOSFET; 2DEG

 

 

8. Magnetism (slides with notes, lecture notes, bare 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 with notes, lecture notes, slides)

• Link: www.superconductors.org
• Fundamental properties and materials
• 1st and 2nd kind of SCs
• Link: Some Abrikosov lattices
• Nobel prize 1986: Scanning Tunneling Microscope
• Link: Nobel Prize 2003 Theory SC
• Thermodynamics of the type I SC state
• Phenomenological description (London theory)
• Link: SC levitation
• Link: SC Levitation 2
• Cooper pairs, microscopic description
• BCS-theory
• Link: Nobelpreis 1972 BCS
• Link: Nobelpreis 1987 Hochtemperatursupraleiter
• SC gap and how to measure it
• Macroscopic wave function, Quantisation
• Link: Emergent universe - SC dance flashmob
• Josephson effect
• Nobel prize 1973: Esaki, Giaever, Josephson
• Link: Nobel laureate vs. grad student: a story about Bardeen and Josephson
• SQUID
• Cuprate superconductors

 

10. Dielectrical and optical properties

• Fundamental properties
• Macroscopic susceptibility and atomic polarizability
• Contributions to the electric polarization
• Plasmons - bulk, surface and nanostructures
• Advanced reading: V. Giannini et al., Nanoplasmonics, Small 2010
• Ferroelectricity
• Multiferroics - coupling of electric and magnetic degrees of freedom