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A two dimensional electronic gas (2DEG) with high mobility of carriers placed in perpendicular magnetic field exhibits the integer and fractional quantum Hall effects. The Landau quantization of electronic levels in 2D system leads to gaps in the density of states. The Fermi energy is then an oscillatory function of the magnetic field, jumping to successively lower Landau levels with the increasing Landau level degeneracy eB/h per spin sub level. The gap in the density of states at the Fermi level is responsible for the integer quantum Hall effect which was first reported in Si MOSFETS at integer filling factors hns/eB, where ns is the 2D carrier density. When electron-electron interactions are taken into account, gaps also occur in the density of states at fractional filling factors leading to the fractional quantum Hall effect, first reported in GaAs heterojunctions. The resistivity of the sample Rxx = 0 while the Hall resistivity Rxy = h/e2 is quantized, where - takes integer 1, 2, 3... or fractional 1/3, 2/3... values. Since the discovery of both the integer and fractional quantum hall effect, the quality of GaAs based samples has been continuously improving. As a consequence, it is now possible t o observe many fractional states in the 0LL as well as in the 1LL.

The physics of interacting electrons at half integer filling factor has intrigued researchers over the past two decades. It was found that the behavior at the first Landau level can be understood in terms of non-interacting composite fermions (CF) at zero magnetic field. Numerous experimental findings confirm this picture, and establish the formation of a non-gaped state at filling factor 1/2. The behavior in the second Landau level is, however, fundamentally different. Early experiments, (...)

Electron-electron interactions in two dimensions dominate in many cases over the single particle physics leading to new collective ground states of the system. The physics in the vicinity of filling factor 1 is particularly rich. The system behaves as a half empty Landau band in which all the electrons have the same orbital quantum number and only the spin degree of freedom remains. At exactly filling factor 1, the predicted ground state is an itinerant quantum Hall ferromagnet , while on (...)