The effective magnetic field of composite fermions has been confirmed by the similarity of the fractional and the integer quantum Hall effects, observation of Fermi sea at half filled Landau level, and measurements of the cyclotron radius.

22.

An extremely high precision measurement of the quantized energies of the cyclotron orbits, or " Landau levels ", of the electron, compared to the quantized energies of the electron's two possible g-factor:

23.

Read was awarded the 2002 Oliver E . Buckley Condensed Matter Prize together with Jainendra Jain and Robert Willet " For theoretical and experimental work establishing the composite fermion model for the half-filled Landau level and other quantized Hall systems"

24.

Electrons form Landau levels in a magnetic field, and the number of filled Landau levels is called the filling factor, given by the expression \ nu = \ rho \ phi _ 0 / B . Composite fermions form Landau-like levels in the effective magnetic field B ^ *, which are called composite fermion Landau levels or \ Lambda levels.

25.

Electrons form Landau levels in a magnetic field, and the number of filled Landau levels is called the filling factor, given by the expression \ nu = \ rho \ phi _ 0 / B . Composite fermions form Landau-like levels in the effective magnetic field B ^ *, which are called composite fermion Landau levels or \ Lambda levels.

26.

Electrons form Landau levels in a magnetic field, and the number of filled Landau levels is called the filling factor, given by the expression \ nu = \ rho \ phi _ 0 / B . Composite fermions form Landau-like levels in the effective magnetic field B ^ *, which are called composite fermion Landau levels or \ Lambda levels.

27.

The quantization of the Hall effect \ sigma _ { xy } at integer multiples ( the " Landau level " ) of the basic quantity e ^ 2 / h ( where " e " is the elementary electric charge and " h " is Planck's constant ) It can usually be observed only in very clean silicon or gallium arsenide solids at temperatures around and very high magnetic fields.

28.

Here \ Psi ^ { \ rm FQHE } _ { \ nu } is the wave function of interacting electrons at filling factor \ nu; \ Psi ^ { \ rm IQHE } _ { \ nu ^ * } is the wave function for weakly interacting electrons at \ nu ^ *; N is the number of electrons or composite fermions; z _ j = x _ j + iy _ j is the coordinate of the j th particle; and P is an operator that projects the wave function into the lowest Landau level.

29.

If we ignore the jellium and mutual Coulomb repulsion between the electrons as a zeroth order approximation, we have an infinitely degenerate lowest Landau level ( LLL ) and with a filling factor of 1 / n, we'd expect that all of the electrons would lie in the LLL . Turning on the interactions, we can make the approximation that all of the electrons lie in the LLL . If \ psi _ 0 is the single particle wavefunction of the LLL state with the lowest orbital angular momentum, then the Laughlin ansatz for the multiparticle wavefunction is

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