- University of Siegen - Department of Physics - Theoretical Quantum Optics Group -

WS2020: Introduction to Theoretical Condensed Matter Physics

Lectures: H. Chau Nguyen (email)
Exercises: Jens Borgermeister (email)
Time and place: 8-10 Friday, Online (Lectures); 16-18 Thursday, Online (Exercises);

Prerequisites

• Basic quantum mechanics
• Linear algebra and analysis

Contents

• General overview of condensed matter physics
• CMP phases, crystals and their symmetry, X-ray scattering
• Phonons, thermal properties, neutron scattering, the Moessbauer's effect
• Electron in the lattices, band-gap theory, tight-binding models, topology
• Basic theory of transport, Hall effect
• Quantum transport, Anderson localisation, quantum Hall effect
• Basic aspects of interacting models

Lectures

Chapter 1: Introduction to condensed matter physics

• Anderson, "More is different," Sience 177 393 (1972)
• Schweber, "Physics, community and the crisis in physical theory," Phys. Today 46 34 (1993)

Chapter 2: The role of ground state and excitations

• Steven Simon's book, Chapter 7.
• Zagoskin's book, few first pages of Chapter 1.

Chapter 3: Crystal structure, X-ray scattering and the reciprocal lattices

• Steven Simon's book, Chapter 12.

Chapter 4: Symmetry of crystals

• Armstrong's book, Chapter 25.

Chapter 5: Oscillatory excitations of crystals - phonons

• Quantum mechanical description of oscillatory excitations (slides, currently password protected due to some copyrighted figures.)
• Thermal properties (video record).
• Neutron scattering (video record). Further reading: Ashcroft and Mermin's book, Chapter 24 and Appendix N; Girvin and Yang's book Chapter 4.

Chapter 6: Electronic degree of freedom

• Bloch theorem (video record).
• Kronig -- Penney model (video record).
• Tight binding models (video record).
• Basic physics of metals, semiconductors and insulators (video record). I highly recommend Steven Simon's book, Chapter 16-18 for further reading!!!
• Peierls' instablity and soliton exictations in polyacetylene (video record). Further reading: Su et al PRB 22 2099 (1980); Girvin's book, Chapter 7.
• Geometry and topology in band theory (1) (video record). Further reading: Girvin's book, Chapter 13.
• Geometry and topology in band theory (2) (video record). Further reading: Girvin's book, Chapter 13.

References

• Steven M. Girvin and Kun Yang, "Modern condensed matter physics," Cambridge University Press 2019.
  This is a modern approach to condensed matter theory, which is also the approach I adopted for this course. The contents of the course are however adapted/simplified so that it is suitable also for advanced undergraduate students.
• Ashcroft and Mermin, "Solid state physics," Thomson 1976.
  This is a somewhat more traditional approach to solid state physics. Occasionally I use this to supply more intuition when necessary.
• Steven H Simon, "The Oxford Solid state basics," Oxford 2019.
Although we do not adopt this approach to our course, it is still a good reference to learn more physical intuition.
• Alexander Zagoskin, "Quantum theory of Many-body systems," Springer 2014.
One can use the first chapters somehow to have a big and coherent picture from single-particle theory to many-particle theory, although most of the time in this course we stay in the single-particle theory.
• Alexander Altland and Ben Simons, "Condensed Matter Field Theory," Oxford 2007.
This is somewhat advanced for our purpose. Yet, here and there one can find good physical insights in the discussions of various physical phenomena.