Condensed Matter Theory 1
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 textbook 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 wavefunction 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
 Bandstructure, Fermisurface, Density of states, Metals, Insulators, Semiconductors
 Semiconductor physics
 Surface states
 Phonons and disorder
 Relativistic corrections  spinorbit 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
 Meanfield theory
 HartreeFock
 Density functional theory
Recommended literature

Ashcroft / Mermin
Solid State Physics 
Kittel
Introduction to Solid State Physics 
Mattuck
A guide to Feynman Diagrams in the ManyBody Problem 
E.N. Economou
Green's Functions in Quantum Physics 
MajlisThe Quantum Theory of Magnetism

Haken / WolfThe 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
Exercise sheets
 sheet 01
 sheet 02
 sheet 03
 sheet 04
 sheet 5
 sheet 6
 sheet 07
 sheet 08
 sheet 09
 sheet 10
 sheet exam
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 
24.10.202228.10.2022  Chapter 3 of the script. Sommerfeld model, Fermi surface, bandstructure 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. Meanfield methods. A short overview of different meanfield 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 bandstructure. 
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
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.
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.