Advanced Solid State Physics

Outline

Electrons

Magnetic effects and
Fermi surfaces

Magnetism

Linear response

Transport

Crystal Physics

Electron-electron
interactions

Quasiparticles

Structural phase
transitions

Landau theory
of second order
phase transitions

Superconductivity

Quantization

Photons

Exam questions

Appendices

Lectures

Books

Course notes

TUG students

      

Magnetic effects and Fermi surfaces

This section begins with a discussion of free electrons in a magnetic field. Classically, the electrons move in a circle in a plane perpendicular to the magnetic field or they spiral along the magntic field lines. (See: Motion of a Charged Particle in a Constant Magnetic Field) Quanutm mechanically, the electron states arrange into Landau levels. (See: The Hamiltonian of a charged particle in a magnetic field and Solutions to the Schrödinger equation for a charged particle in a magnetic field). The presence of a magnetic field modifies the density of states of of the free elelctrons in such a way that all of the thermodynamic properties oscillate with $1/B$. (See: Thermodynamic properties of free electrons in a magnetic field) Oscillations of the magnetization with $1/B$ are called de Haas - van Alphen oscillations and the oscillations of the electrical resistivity are called the Shubnikov - de Haas oscillations. At high magnetic fields only a few Landau levels are occupied and the Shubnikov - de Haas oscillations develop into the Quantum Hall effect.

Reading
Kittel chapter 9: Fermi surfaces and metals
Kittel Appendix G: Vector potential, field momentum, and gauge transformations
or Gross and Marx: 9.7.1: Freie Ladungsträger