Hi! I'm having trouble understanding the quantum hall effect, that is, the fact that the Hall resistance versus magnetic field curve has regions where it drops to zero, and the longitudinal resistance versus magnetic field curve features plateaus. When the filling factor is an integer, this corresponds to the situation where the highest occupied Landau level is completely filled, which means that the Fermi energy lies between an occupied Landau level and an unoccupied Landau level. How is it that this leads to the plateaus and zeros in the resistances? Is it as simple as electrons not being able to be scattered because there is nowhere for them to scatter to, at low temperatures and high B fields? How do the impurities in the lattice, which trap electrons in their potentials, contribute to the Hall effect? I also don't get the fractional quantum hall effect. All the sources I've been looking at say that it is the result of electron correlation or interaction, and it corresponds to the case where the Fermi energy is partway up a Landau level. But how does this electron interaction give rise to the plateaus in the longitudinal resistance, and the zeros in the transverse resistance? Thanks a lot!!