On the extended states in the Quantum Hall regime and in zero magnetic field

Abstract

For a two dimensional electron system in a strong perpendicular magnetic field B, there are extended states at each Landau level. We show that if the inverse compressibility is negative, then the extended states float downward in energy when B decreases. We set up a condition for the case where all extended states are below the fermi energy in the low B limit. The condition may explain why a conducting state has been observed in a high mobility Si-Mosfet but so far not in high mobility n-GaAs.