HOW WELL IS THE INTEGER QUANTUM HALL-EFFECT UNDERSTOOD

From the basic experimental facts, a list of requirements on a satisfactory microscopic theory of the integer quantum Hall effect (IQHE) is established. These requirements seem to be satisfied by a recent new approach, which is based on general properties of the solutions of the time-dependent Schrodinger equation of a disordered system in a macroscopic electric field and their implications to the dynamic behaviour of the electrons in a broadened Landau band. From this a new picture of the IQHE arises. It appears that also a consistent explanation of the basic related phenomena is achieved, like the electric field dependence of the mobility edges and the breakdown of the IQHE. The main findings of this new approach are discussed and confronted with previous theories, and it is found that these theories do not fulfil the established requirements. Finally, some experimental aspects are mentioned which still remain not very well understood and possible ways for further progress are proposed.