Condensed Matter Theory

Department > Lectures > Winter term 2023/2024 > Condensed Matter Theory

Condensed Matter Theory

winter term 2023/2024
Lecturer: Maurits W. Haverkort
Link to LSF
29 participants

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

Script to the lecture
Script 18 October 2023
Group and phase velocity
The Mathematica notebook shows the time evolution of a Wave-packet. The gif file is the result and shows the propagation of the density and of the wave with different velocities. The script in chapter 4.2.3 discusses the group and phase velocity
Propagation_of_Gaussian_wave_packets.nb
WavePackets.gif
Quantum_Physics_2023.pdf
Group theory
Here you can find the script of my and Martin Brass lecture on group theory. I furthermore added a chapter from a textbook by Ballhausen. The book chapter is not mathematical rigorous, but shows a very quick introduction to the use of group theory.
Group_theory.pdf
Ballhausen_chapter3.pdf

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

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.