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

TL;DR

This paper investigates the behavior of extended electronic states in two-dimensional systems under magnetic fields, proposing conditions for their energy evolution and explaining experimental differences in conductance.

Contribution

It introduces a condition linking negative inverse compressibility to the downward energy shift of extended states as magnetic field decreases.

Findings

Extended states float downward in energy when B decreases with negative inverse compressibility.

A condition is proposed for all extended states to be below the Fermi energy at low B.

The theory explains the presence of conducting states in high mobility Si-MOSFETs but not in n-GaAs.

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.