Universal flow diagram for the magnetoconductance in disordered GaAs layers

TL;DR

This study demonstrates that the magnetoconductance flow lines in disordered GaAs layers follow a universal scaling theory, revealing a semicircular separatrix that distinguishes insulating and quantum Hall states, consistent with duality symmetry.

Contribution

It provides experimental validation of a universal flow diagram for magnetoconductance in disordered GaAs, confirming theoretical predictions based on duality symmetry.

Findings

Flow lines are well described by the universal scaling theory.

The separatrix G_{xy}=1 divides insulating and QHE states.

Flow merging occurs along a semicircle separatrix.

Abstract

The temperature driven flow lines of the diagonal and Hall magnetoconductance data (G_{xx},G_{xy}) are studied in heavily Si-doped, disordered GaAs layers with different thicknesses. The flow lines are quantitatively well described by a recent universal scaling theory developed for the case of duality symmetry. The separatrix G_{xy}=1 (in units e^2/h) separates an insulating state from a spin-degenerate quantum Hall effect (QHE) state. The merging into the insulator or the QHE state at low temperatures happens along a semicircle separatrix G_{xx}^2+(G_{xy}-1)^2=1 which is divided by an unstable fixed point at (G_{xx},G_{xy})=(1,1).