## Lecture: Solid State Theory

### Winter Term 2012/13

Monday, 12:00 - 13:30, and Wednesday 16:00 - 17:30,
Seminarraum Theorie

This lecture gives an introduction to the theoretical concepts
for the description of solids. The ultimate aim is the
understanding of the multitude of physical phenomena - such
as metallic vs. insulating behaviour, magnetism, superconductivity,
etc. - as observed in solid state materials, along with the
calculation of physical properties - such as conductivities,
specific heat, etc. To this end we develop theoretical
approaches which can deal with a macroscopic number of
interacting quantum objects, with the focus on electrons
and quantized lattice vibrations (phonons).

Module description
of the primary area of specialization
`Solid State Theory/Computational Physics'

**Contents:**
- introduction
- structure and periodicity

1.1 some basics

1.2 the reciprocal lattice

1.3 periodic functions
- separation of lattice and electron dynamics

2.1 the general solid state Hamiltonian

2.2 adiabatic approximation (Born-Oppenheimer approximation)
- phonons

3.1 the harmonic approximation

3.2 translational invariance

3.3 boundary conditions

3.4 phonons: quantized lattice vibrations

3.5 thermodynamics of lattice vibrations

3.6 phonon density of states
- electrons on a lattice (non-interacting)

4.1 Bloch theorem

4.2 the nearly-free electron model

4.3 the effective mass

4.4 the tight-binding model

4.5 electron density of states and Fermi surface

4.6 thermodynamics of electrons on a lattice
- electron-electron interaction

5.1 the solid-state Hamiltonian in second quantization

5.2 the Hubbard model

script

**Literature:**
- Gerd Czycholl

Theoretische Festkörperphysik
- Jeno Solyom

Fundamentals of the Physics of Solids,
Volume 1 - Structure and Dynamics

Springer-Verlag
- J.M. Ziman

Principles of the Theory of Solids

Cambridge University Press

**Tutorials:**

Wednesdays, 16:00 - 17:30, every second week

Dates: Oct 17, Oct 31, Nov 21, Nov 28, Dec 12, Jan 9, Jan 23

Seminarraum Theorie

Exercises
Solutions can be returned in groups of up to three students.

Requirements for the admission to the module exam
- primary and secondary area of specialization:
- active participation in the tutorials
- at least 50% of the points from the exercises

- elective subject:
- active participation in the tutorials

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