Elementary Theory: the Incompressible Quantum Fluid
The effect occurs when electrons are at a particular density, determined by the magnetic field strength. The separation between neighboring electrons locks in at particular values.
The fractional quantum Hall effect looks to the eye like the integral quantum Hall effect, except that the Hall conductance, in the case of the 1/3 step, is 1/3 e 2 h. There is a plateau. Changing the electron density a small amount does not alter the Hall conductance, but changing it a large amount does.
The 1/3 effect turns on in GaAs at about 1 K when the magnetic field is 15 Tesla.
The effect occurs only in the cleanest samples. Excessive dirt destroys it.
Other fractions (2/5, 2/7, …) also occur but they are more easily destroyed by dirt and require lower temperatures to be observed. The most ‘stable’ states have small denominators.
KeywordsWave Function Radial Distribution Function Landau Level Elementary Theory Quantum Hall Effect
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