Fakultät > Vorlesungen > Wintersemester 2021/2022 > Condensed Matter Theory

Condensed Matter Theory

Wintersemester 2021/2022
Dozent: Maurits W. Haverkort
Link zum LSF
E-Learning
30 Teilnehmer/innen

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Lecture content

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

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

The lecture script and videos are available on Moodle.

If you find errors in the script, please report them to me. The script will be updated regularly, but don't expect major changes. The script is quite extensive, and explicitly goes through the calculation of several examples. I will discuss in the lecture where to focus on.

You can find videos of the lecture content on youtube

Material discussed

 

18.10.2021 - 22.10.2021

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
25.10.2021-29.10.2021 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 ?
1.11.2021 - 5.11.2021 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
8.11.2021 - 12.11.2021 Chapter 5 of the script. Mean-field methods. A short overview of different mean-field theories used to obtain effective potentials from interacting Hamiltonians
15.11.2021 - 19.11.2021 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.
22.11.2021 - 26.11.2021 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.
29.11.2021 - 3.12.2021 Chapter 7 of the script. Green's functions. Impurity scattering - Become fluent in working with Green's functions.
6.12.2021 - 10.12.2021 Finish chapter 7. Videos 7.7 to 7.12 (https://www.youtube.com/playlist?list=PLhOEg5oWOoSXlUI4Lk6PtFpAjoPTxW2wQ) Meeting for questions - Friday via Zoom
13.12.2021 - 17.12.2021 Chapter 8 of the script. Self energy due to disorder. Video 8.1 https://www.youtube.com/playlist?list=PLhOEg5oWOoSVn-mQz5U-e6N_3_dIXySd1 Meeting on Friday via Zoom
20.12.2021 - 24.12.2021 Only tutorials
10.01.2022 - 15.01.2022 Chapter 9 of the script, Surface states
17.01.2022 - 22.01.2022 Chapter 10 of the script, Relativisitc effect. (Single lecture, no part of the exam). Chapter 11 of the script, Phase transitions. 
24.01.2022 - 29.01.2022 Chapter 11 - Topological states and surface states - Chapter 12 - Response theory
31.01.2022 - 04.02.2022 Chapter 12 - Response theory
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Condensed Matter Theory
Wintersemester 2021/2022
Haverkort
Link zum LSF
E-Learning
30 Teilnehmer/innen
Besides the lectures in real life we will provide videos via Moodle. You need the following password to register for the Moodle site. _CMT_
For questions outside the lecture period you can find us on Rocket Chat: https://uebungen.physik.uni-heidelberg.de/chat
The first lecture will be on Monday the 18-th 9:15. Please be aware that you need to be either vaccinated, cured or tested on the day of the lecture ("3G") and wear a mask. If you can not make it to the institute you can follow us via Zoom.
  • Monday, from 9:15 to 11:00 tutorials in Philos.-weg 19 / SR.
  • Wednesday from 9:15 to 11:00 lecture in Philos.-weg 19 / SR.
  • Friday from 9:15 to 11:00 lecture INF 227 / HS 2.
  • First lecture on Monday the 18-th of October
  • No lecture on Wednesday the 20-th of October
  • First homework due on Friday the 5-th of November, discussed on Monday the 8-th of November