Advanced Solid State Physics
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.