Introduction to quantum Hall effects

The quantum Hall effect is a set of phenomena observed at low temperature i n a two-dimensional electron gas subject to a strong perpendicular magnetic field. It manifests itself as a quantization of the nondiagonal elements ( rho (xy)) of the resistivity tensor accompanied by simultaneous vanishing r ho (xy) for ranges of the magnetic field. For the integer quantum Hall effe ct rho (xy) = h/ve(2), where h is the Planck constant, e - charge of an ele ctron and v is an integer, while for the fractional quantum Hall effect v i s a simple fraction. In spite of similar phenomenology deep and profound di fferences exist between these two effects, In the lecture the precision of the Hall quantization in the integer quantum Hall effect and briefly new ty pes of quantum fluids observed in the fractional quantum Hall effect are di scussed. Some recent theoretical and experimental discoveries connected wit h quantum Hall liquids are also mentioned.