The integral quantum Hall effect and fractional quantum Hall effect are two of the most remarkable physical phenomena to be discovered in solid state physics in recent years. In many respects, the two phenomena share very similar underlying physical characteristics and concepts, for instance, the two-dimensionality of the system, the quantization of the Hall resistance in units of h/e 2 with a simultaneous vanishing of the longitudinal resistance, and the interplay between disorder and the magnetic field giving rise to the existence of extended states. In other respects, they encompass entirely different physical principles and ideas. In particular, the IQHE is believed to be a manifestation of the transport properties of a noninteracting, charged-particle system, in the presence of a strong perpendicular magnetic field, whereas the FQHE results from a repulsive interaction between particles, giving rise to a novel form of many-body ground state. Moreover, the mobile (non-localized) elementary excitations must carry fractional charge and lie at a finite energy above the ground state. These fractionally charged excitations are thought to obey unusual statistics which are neither Fermi nor Bose-Einstein.
KeywordsVortex Crystallization Torque Shrinkage GaAs
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