Disorder and Integral Quantum Hall Effect

The quantum Hall conductance of a disordered two-dimensional gas of non-interacting electrons is re-examined for its integrity against disorder in the limit of no mixing between different Landau levels. The exact one-electron eigenstates of the disordered system are shown to be current carrying, with exactly the same Hall current as in the absence of disorder. There are no localized states. Accordingly, each extensively degenerate Landau level, now broadened out by the disorder, continues to contribute exactly one quantum of Hall conductance ($e^2/2\pi\hbar$). In the absence of any localized (non-current carrying) states, the Hall plateaus can now arise only through an actual gap in the density of states separating the broadened Landau levels. Implications for 2D localization are discussed.