Fakultät > Vorlesungen > Wintersemester 2023/2024 > Condensed Matter Theory

Condensed Matter Theory

Wintersemester 2023/2024
Dozent: Maurits W. Haverkort
Link zum LSF
29 Teilnehmer/innen

Condensed Matter Theory

Condensed Matter Theory I:
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

Material

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
  • There is a script that acompanies the lecture. Feedback and typos are most welcome.

Material discussed

 

18.10.2023 - 22.10.2023

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
23.10.2023-27.10.2023 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 ?
30.10.2023 - 3.11.2023 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
6.11.2023 - 10.11.2023 Chapter 5 of the script. Mean-field methods. A short overview of different mean-field theories used to obtain effective potentials from interacting Hamiltonians
13.11.2023 - 17.11.2023 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.
20.11.2023 - 24.11.2023 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.
27.11.2023 - 1.12.2023 Chapter 7 of the script. Green's functions. Impurity scattering - Become fluent in working with Green's functions.
4.12.2023 - 8.12.2023 Finish chapter 7. Chapter 8 of the script. Self energy due to disorder.
11.12.2023 - 16.12.2023 Chapter 9 of the script, Surface states
18.12.2023 - 22.12.2023 Chapter 10 of the script, Relativisitc effect. (Single lecture, no part of the exam). 
8.01.2024 - 13.01.2024 Chapter 11 of the script, Phase transitions.  - Topological states and surface states - 
15.01.2024 - 20.01.2024 Chapter 12 - Response theory
22.01.2024 - 27.01.2024 Chapter 12 - Response theory
29.01.2024 - 02.02.2024 Time to study
07.02.2024 Exam on Wednesay 07.02.2024 9:00 to 11:00
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Schedule
  • The lectures are on Wednesday and Friday from 9:15 to 11:00 in Philosphenweg 19. 
  • The tutorials are on Monday from 9:15 to 11:00 in Philosophenweg 19.
  • The first lecture is on Wednesday the 18th.
  • The first tutorial is on Monday the 30th, we meet on Monday the 23rd for a lecture.
  • There will be no lecture on Friday the 20th, instead we will have a lecture on Monday the 23rd.
The lectures will be in person. For those who are not able to join, we will stream the lectures via Zoom. I however do highly recommend you to be present in real life. The atmosphere and view is nice. You can also find recordings from previous years on Youtube.