If Zeeman splitting is included, each Landau level splits into a pair, one for spin up electrons and the other for spin down electrons.
Zeeman splitting has a significant effect on the Landau levels because their energy scales are the same, "'? " } }.
When the external magnetic field B is increased in an isolated system, the Landau levels expand, and eventually " fall off " the Fermi surface.
Effects of Landau levels are only observed when the mean thermal energy is smaller than the energy level separation,, meaning low temperatures and strong magnetic fields.
The speed formula comes from setting the classical kinetic energy equal to the spacing between Landau levels in the quantum treatment of a charged particle in a magnetic field.
When these conditions are satisfied, an electron will complete its cyclotron orbit without engaging in a collision, at which point it is said to be in a well-defined Landau level.
Here the second Landau level is half full, but the state cannot be a Fermi sea of composite fermions, because the Fermi sea is gapless and does not show quantum Hall effect.
The occupation of the highest Landau level ranges from completely full to entirely empty, leading to oscillations in various electronic properties ( see de Haas van Alphen effect and Shubnikov de Haas effect ).
He developed a theory of " composite fermions ", which can be used to explain properties of free electron gas at high magnetic fields, in quantum hall liquids and half-filled Landau levels.
In ultrastrong magnetic fields, the magnetic-field interaction may exceed H _ 0, in which case the atom can no longer exist in its normal meaning, and one talks about Landau levels instead.