Condensed Matter Theory 1

winter term 2022/2023
Lecturer: Haverkort
Link to LSF
24 participants
The complexity of 1023 particles interacting with each other in a solid give rise to many emergent phenomena one would not predict from the simple interactions between two electrons. In this lecture we will, starting from simple models and theories work our way into the contemporary theory of many particle physics. 
The lecture follows for a large part the textbook of Ashcroft and Mermin, with one big difference. The formentioned text-book is based on a text over 50 years old. During the last decades new methods have emerged, often removing the need to know the full wave-function of the system to answer the problem, by using Green's functions. Whenever possible the later will be used within this lecture.
Concepts of many particle systems discused are:
  • The Drude Theory of Metals
  • The Sommerfeld Theory of Metals
  • Electrons in a periodic potential
  • Tight binding
  • Band-structure, Fermi-surface, Density of states, Metals, Insulators, Semiconductors
  • Semiconductor physics
  • Surface states
  • Phonons and disorder
  • Relativistic corrections - spin-orbit coupling
  • Phase transitions and topology
  • Response functions
Theoretical / Mathematical tools used will be
  • Second quantization
  • Green's functions (on an independent particle level)
  • Self energy (for surface states and disorder)

Levels of theory discussed will be

  • Mean-field theory
  • Hartree-Fock
  • Density functional theory

Recommended literature

  • Ashcroft / Mermin
    Solid State Physics
  • Kittel
    Introduction to Solid State Physics
  • Mattuck
    A guide to Feynman Diagrams in the Many-Body Problem
  • E.N. Economou
    Green's Functions in Quantum Physics
  • Majlis
    The Quantum Theory of Magnetism
  • Haken / Wolf
    The Physics of Atoms and Quanta

Practice groups

  • Group 01 (Banerjee Sreya)
    15 participants
    Philosophenweg 19 SR, Mon 9:15 - 11:00
  • Group 02 (Sina Shokri)
    9 participants
    Philosoph.-weg 19 / SR, Mon 11:15 - 13:00

Material discussed


17.10.2022 - 21.10.2022

Chapter 1 and 2 plus appendix A of the script. 

Chapter 1 + appendix A: Introduction and repetition of Quantum mechanics and second quantisation. The Hamiltonian of interest for condensed matter systems. Complexity of many electron system and emergent behaviour.

Chapter 2: Drude model, Scattering length, Ohms law and Specific Heat

24.10.2022-28.10.2022 Chapter 3 of the script. Sommerfeld model, Fermi surface, band-structure or energy momentum dispersion and density of states. Solution to the specific heat problem in the Drude model. Scattering time and the probelm of near scattering length: Why do atomic nuclei in a periodic lattice appearently not scatter electrons ?
31.10.2022 - 4.11.2022 Chapter 4 (and appendix B) of the script. Periodic potentials, Bloch states, Bloch's theorm, crystal momentum. (Real and reciprocal lattice vectors) -- I assume this chapter is a repetition of lectures you heard before
7.11.2022 - 11.11.2022 Chapter 5 of the script. Mean-field methods. A short overview of different mean-field theories used to obtain effective potentials from interacting Hamiltonians
14.11.2022 - 18.11.2022 Chapter 6 of the script. Tight binding theory. Dual nature of Tight binding model and free electron model. Sign of hopping integrals, angular dependence of hopping integrals. Tight binding description of free electron bands.
21.11.2022 - 25.11.2022 Chapter 6 and 7 of the script. Wannier functions, band character and partial density of states + Definitions of Green's functions frequency and time doman and relation to band-structure.
28.11.2022 - 2.12.2022 Chapter 7 of the script. Green's functions. Impurity scattering - Become fluent in working with Green's functions.
5.12.2022 - 9.12.2022 Chapter 7 of the script
12.12.2022 - 16.12.2022 Chapter 8 of the script. Self energy due to disorder. 
19.12.2022 - 23.12.2022 Chapter 10 of the script, Relativisitc effect. (Single lecture, no part of the exam).
9.01.2023 - 14.01.2023 Chapter 9 of the script, Surface states
16.01.2023 - 21.01.2023  Chapter 11 of the script, Phase transitions. Topological states and surface states
22.01.2023 - 28.01.2023 Chapter 12 - Response theory
30.01.2023 - 03.02.2023 Chapter 12 - Response theory
6.02.2023 - 10.02.2023 Time to study
13.02.2023 - 17.02.2023 Exam
Condensed Matter Theory 1
winter term 2022/2023
Link zum LSF
24 participants
Besides the lectures in real life you can find Youtube videos of the topics discussed.
The lectures will be streamed via Zoom, but we do advise to be present in real life.
The lecture series contains lectures on Wednesday and Friday morning, from 9:15 to 11:00 and tutorial sessions on Monday morning.
The first lecture will be on Wednesday the 19th of October.