Resistance fluctuations in quantum Hall transitions: Network of compressible-incompressible regions

Abstract

Resistance fluctuations in integer and fractional quantum Hall transitions are studied in modulation-doped ${\mathrm{Al}}_{0.3}{\mathrm{Ga}}_{0.7}\mathrm{A}\mathrm{s}/\mathrm{G}\mathrm{a}\mathrm{A}\mathrm{s}$ heterostructures. We examine the role of coherence in the fluctuations by investigating the conductance through two scattering regions that are spatially separated but interact quantum-mechanically with each other. Though the conductor is in a coherent regime, the phase coherence is found to play an insignificant role in determining the observed pattern of fluctuations. In transition regions where the average filling factor of Landau levels takes a noninteger value, $n\ensuremath{-}1l\ensuremath{\nu}ln,$ the electron system splits into incompressible subregions of $\ensuremath{\nu}=n$ and those of $\ensuremath{\nu}=n\ensuremath{-}1,$ which are separated by percolating compressible strips. Irregular evolution of the network of compressible strips is suggested to be the origin of the resistance fluctuations in integer quantum Hall transitions. A similar mechanism is also suggested for fractional quantum-Hall transitions.