What is landau level?

Landau levels are quantized energy levels that arise when charged particles are placed in a uniform magnetic field. They are named after the German physicist Lev Landau who first described them in 1930. In a magnetic field, charged particles such as electrons or protons experience a force perpendicular to their velocity, causing them to move in circular orbits. The energy of these orbits is quantized into Landau levels, which are separated by a constant energy spacing.

The number of Landau levels present is proportional to the strength of the magnetic field, with the energy spacing between levels increasing as the magnetic field strength increases. The Landau levels are also affected by the geometry of the system, such as the shape of the electric potential that the charged particles experience. In some materials, the Landau levels can lead to interesting effects such as quantum Hall effect and fractional quantum Hall effect, which have important applications in electronic transport and metrology.