J ul 1 99 6 Disorder and Integral Quantum Hall Effect

The quantum Hall conductance of a disordered two-dimensional gas of non-interacting electrons is reexamined 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 /2π¯ h). 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. The Hall conductance σ xy of a two-dimensional spin-polarized electron gas (2DEG) is well known to be stepped in units of the quantum of conductance e 2 /2π¯ h. This is the Integral Quantum Hall Effect (IQHE). 1,2 Such a 2D electron system obtains as an inversion/accumulation layer in a gated Si MOS-FET (metal-oxide semiconductor field effect transistor) or a modulation doped GaAs-AlGaAs heterostructure. 3 The quantized conductance steps are observed experimentally as function of the strength of the external magnetic field (B) applied perpendicular to the plane of the 2DEG. The field tunes the density-of-states in the Landau levels, and thus controls their filling for a fixed areal 1