Physics:Quantum Landau levels
Quantum Landau levels are discrete energy levels of a charged particle moving in a plane under a uniform magnetic field. They arise because the classical circular motion of a charge in a magnetic field becomes quantized in quantum mechanics.[1]
The levels are named after Lev Landau, who developed the theory of diamagnetism for free electrons. Landau levels are central to two-dimensional electron gases, magnetotransport, de Haas-van Alphen oscillations, and the quantum Hall effect.
Quantization in a magnetic field
A charged particle in a magnetic field undergoes cyclotron motion. In quantum theory, only certain orbital energies are allowed, producing equally spaced Landau levels for an ideal nonrelativistic system.
Each Landau level can have a large degeneracy, meaning many states share the same energy. This degeneracy is tied to magnetic flux through the sample and is crucial for quantum Hall physics.
Condensed matter role
In materials, Landau levels become visible through oscillations in electronic properties as magnetic field changes. In clean two-dimensional systems, filled Landau levels lead to quantized Hall conductance.
Graphene and other Dirac materials show modified Landau-level structures because their quasiparticles obey relativistic-like equations.
See also
- Physics:Quantum Hall effect
- Physics:Quantum Fermi surfaces
- Physics:Quantum Band structure
- Biography:Lev Landau
References
Source attribution: Physics:Quantum Landau levels