Universality of Anderson Localization Transitions in the Integer and Fractional Quantum Hall Regime

Abstract

Understanding the interplay between electronic interactions and disorder-induced localization has been a longstanding quest in the physics of quantum materials. One of the most convincing demonstrations of the scaling theory of localization for noninteracting electrons has come from plateau transitions in the integer quantum Hall effect with short-range disorder, wherein the localization length diverges as the critical filling factor is approached with a measured scaling exponent close to the theoretical estimates. In this work, we extend this physics to the fractional quantum Hall effect, a paradigmatic phenomenon arising from a confluence of interaction, disorder, and topology. We employ high-mobility trilayer graphene devices where the transport is dominated by short-range impurity scattering, and the extent of Landau level mixing can be varied by a perpendicular electric field. Our principal finding is that the plateau-to-plateau transitions from N+1/3 to N+2/5 and from N+2/5 to N+3/7 fractional states are governed by a universal scaling exponent, which is identical to that for the integer plateau transitions and is independent of the perpendicular electric field. These observations and the values of the critical filling factors are consistent with a description in terms of Anderson localization-delocalization transitions of weakly interacting electron-flux bound states called composite Fermions. This points to a universal effective physics underlying fractional and integer plateau-to-plateau transitions independent of the quasiparticle statistics of the phases and unaffected by weak Landau level mixing. Besides clarifying the conditions for the realization of the scaling regime for composite fermions, the work opens the possibility of exploring a wide variety of plateau transitions realized in graphene, including the fractional anomalous Hall phases and non-abelian FQH states