Landau level

A Landau level is a quantized energy level for a charged particle moving in a uniform magnetic field. The levels arise because the field confines motion perpendicular to itself into quantized cyclotron orbits.

Cyclotron frequency: The angular frequency at which a charged particle orbits in a magnetic field. It sets the spacing between adjacent Landau levels.
Cyclotron orbit: The circular or helical trajectory of a charged particle in a magnetic field. Quantization replaces its classical transverse orbit with discrete orbital states.
Quantum Hall effect: The quantization of electrical Hall conductance in a two-dimensional electron system at low temperature and strong magnetic field. Its conductance plateaus emerge as Landau levels fill.
Dirac Landau level: A Landau level of a particle governed by a Dirac-like energy–momentum relation. Its energy spacing differs from the equally spaced levels of a conventional parabolic band.
Magnetic length: A characteristic length scale for quantum motion in a magnetic field, set by the magnetic flux quantum. It sets the spatial scale of Landau-level wavefunctions.
Magnetic flux quantum: The quantum of magnetic flux associated with a charged quantum system. It determines the number of distinct orbit centers per area in a Landau level.
Integer quantum Hall effect: The quantum Hall effect produced by the filling of integer numbers of Landau levels. It is the direct transport signature of filled, noninteracting Landau levels.
Spin Landau level: An energy level that includes both orbital Landau quantization and spin coupling to a magnetic field. Spin splitting can create distinct branches beyond the orbital level structure.
Harmonic oscillator: A system whose restoring force is proportional to displacement and whose quantum energies are equally spaced. The transverse Landau-level spectrum has the same mathematics as a quantum harmonic oscillator.
Degeneracy (physics): The number of distinct quantum states that share the same energy. Each Landau level contains many states with identical energy.

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