New insight into the integer quantum Hall effect

Abstract

By considering the degeneracies of the localized and extended states separately we have investigated the integer quantum Hall effect (IQHE) in terms of fraction of extended states in a Landau subband. The IQHE is found to manifest itself as saw-tooth oscillations in the number density of the extended electrons as a function of magnetic field. Preliminary results of an experiment are also presented that support this picture. It is found that contrary to the traditional theoretical belief, the extended states form a non-vanishing fraction of the states in a Landau subband. Significantly it is shown that if this was not so, the IQHE would not arise in the first place. This result is relevant in connection with the long standing question of nature of transition between plateaus, and also the recent discovery of intriguing electron density driven metal-insulator transition in two-dimensional systems. The results also show that extended states float up in energy in addition to being systematically destroyed as the magnetic field is reduced, and that the system can become completely localized at a nonzero magnetic field.