Fakultät > Vorlesungen > Wintersemester 2022/2023 > Condensed Matter Theory 1

Condensed Matter Theory 1

Wintersemester 2022/2023
Dozent: Haverkort
Link zum LSF

WS22-CMT1
24 Teilnehmer/innen

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

Übungsgruppen

Gruppe 01 (Banerjee Sreya)
15 Teilnehmer/innen
Philosophenweg 19 SR, Mo 9:15 - 11:00
Gruppe 02 (Sina Shokri)
9 Teilnehmer/innen
Philosoph.-weg 19 / SR, Mo 11:15 - 13:00

Materialien

Übungsblätter

01
- Exercise1.pdf
02
- Exercise2.pdf
03
- Exercise3.pdf
- Bandstructure of Graphene free electron like.nb
04
- Exercice4.pdf
5
- Exercice5.pdf
6
- Exercise6.pdf
07
- Exercise7.pdf
08
- Exercise8.pdf
09
- problem9.pdf
10
- Exercise10.pdf
exam
- Exam_2023_02_15.pdf

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