Impact of Disorder on the5/2Fractional Quantum Hall State

Abstract

We compare the energy gap of the $\ensuremath{\nu}=5/2$ fractional quantum Hall effect state obtained in conventional high mobility modulation-doped quantum-well samples with those obtained in high quality GaAs transistors (heterojunction insulated gate field-effect transistors). We are able to identify the different roles that long-range and short-range disorders play in the $5/2$ state and observe that the long-range potential fluctuations are more detrimental to the strength of the $5/2$ state than short-range potential disorder.