Condensed Matter Theory I

Lecture contents

Introduction to solid state physics. The complexity of 10²³ particles interacting with each other in a solid gives 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 theores work our way into the contemporary theory of many particle physics. 

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
• Relativistic corrections - spin-orbit coupling
• Phase transitions and topology

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

• Hartree-Fock
• Density functional theory

Material

• 17_10_18_Introduction.pdf
• 17_10_18_Introduction_More_is_different.pptx
• 17_10_20_Drude_model_of_metals.pdf
• 17_11_03_Sommerfeld_theory_of_metals_and_second_quantization.pdf
• 17_11_15_Sommerfeld_theory_of_metals.pdf
• 17_11_17_Periodic_potentials.pdf
• 17_11_22_Hartree_Hartree-Fock_and_Local_density_approximation.pdf
• 17_11_24_Tight_binding.pdf
• 17_12_01_Tight_binding_Peierls_transition.pdf
• 17_12_06_Tigth_binding_of_Graphene.pdf
• 17_12_08_Slater_Koster_Table_one.nb
• 17_12_08_Slater_Koster_Table_one.pdf
• 17_12_08_TIght_binding_examples.pptx
• 17_12_08_notes_slater_koster_tight_binding.nb
• 17_12_08_notes_slater_koster_tight_binding.pdf
• 17_12_13_Normal_state_properties_of_High_temperature_Superconducting_Cuprates.pdf
• 17_12_15_Greens_functions_for_independent_particles.pdf
• 17_12_20_Single_impurity_in_tight_binding_model.pdf
• 17_12_22_Greens_functions_using_continued_fractions.pdf
• 18_01_09_Cooper_instability.pdf
• 18_01_12_Self_energy_due_to_disorder.pdf
• 18_01_17_Surface_states.pdf
• 18_01_24_Topological_Phases.pdf
• 18_01_26_Topological_surface_states.pdf
• 18_01_26_Topological_surface_states.pptx

Exercise sheets

• 01
  
  • Exercise1.pdf
• 02
  
  • Exercise2.pdf
• 03
  
  • Exercise3.pdf
• 04
  
  • Exercise4.pdf
• 05
  
  • Exercise5.pdf
• 06
  
  • Exercise6.pdf
• 07
  
  • Exercise7.pdf
• 08
  
  • Exercise8.pdf
• 09
  
  • Exercise9.pdf

Practice groups

• Group 01 (Nicolo Defenu)
  11 participants
  Philos.-weg 16 / SR, Mon 9:15 - 11:00

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

The lecturenotes will be made available as the lecture progressess, they however should not be your only source of information.

Assumed background

It is assumed students have successfully finnesed the following lectures

• Theoretical Statistical Physics
• Experimentalphysic V - Molekül- und Festkörperphysik