Universal behaviour in the floating up of quantum Hall extended states as B -> 0

Abstract

We investigate the relationship between the quantum Hall extended states and the apparent B=0 `metal'-insulator transition in extremely low density, high quality two-dimensional n-GaAs systems (μ_{peak} ~ 2 x 10^7 cm^2/Vs). The combination of small effective mass and high quality allow us to resolve the continued floating up in energy of the extended states down to very low magnetic fields, B=0.015T, despite an apparent `metal'-insulator transition at B = 0. We present a modified global phase diagram which brings together conflicting data in the literature from different material systems, and reconciles the differences as to the fate of the extended states as B -> 0.