Lecture: Solid State Theory

Priv.-Doz. Dr. Ralf Bulla

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'

  1. introduction
  2. structure and periodicity
    1.1 some basics
    1.2 the reciprocal lattice
    1.3 periodic functions
  3. separation of lattice and electron dynamics
    2.1 the general solid state Hamiltonian
    2.2 adiabatic approximation (Born-Oppenheimer approximation)
  4. 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
  5. 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
  6. electron-electron interaction
    5.1 the solid-state Hamiltonian in second quantization
    5.2 the Hubbard model


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

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