0_3077    The topological aspects of the quantum Hall effect are in the focus of many investigations on systems like graphene and graphene Moiré superlattices. The few recent studies of Fractional Quantum Hall (FQH) states in graphene superlattices have mainly been focused lowest Landau level (LL) states. One of the models which described the FQH states is that of the composite fermions (CFs), quasiparticles originating from the electron mutual interaction in the magnetic field. In this model an even number of magnetic flux quanta attached to each electron gives the fractional state with filling factor ν = p/(2mp±1), with m and p positive integers, and the electron-electron interaction is incorporated into the CFs themselves. The FQH states for the electrons are interpreted as the integer quantum Hall (IQH) states of CFs.   To explores the nature of the FQH states in graphene superlattices, we measured magnetotransport up to 30 T in a graphene hexagonal boron nitride heterostructure, observing fractional states at unusual filling ν as the 4/11, 5/13 and 6/17. These states cannot be described by the standard series for the CFs, in other words they cannot be seen as IQH states of CFs. These fragile states go beyond the model of weakly interacting composite fermions, since they likely arise from an FQH effect of CFs themselves.¹ The 4/11 and 6/17 states are under recent intense investigation, due to their possible parton wavefunction with underlying topological order; the parton model to generalize the concept of CFs, building a wider class of FQH wave functions that explain these unconventional fractional states. In the parton model, the electron is divided into k partons, and unusual fractional states are built placing each parton in an IQH state. The effective magnetic field experienced by the partons can be antiparallel to that seen by the electrons. The partons are non-physical objects that should be stuck back together to recover the electrons. The parton construction gets the standard states of CFs, as well as more general states that do not bring by themselves to an interpretation in terms of composite fermions, such as states that support non-Abelian excitations in multilayer graphene².

1. A.C. Balram, Abelian parton state for the ν = 4/11 fractional quantum Hall effect, Phys. Rev. B 103, 155103 (2021); A. C. Balram and A. Wójs, Parton wave function for the fractional quantum Hall effect at ν = 6/17, Phys. Rev. Research 3, 033087 (2021).
2. Y.-H. Wu, T. Shi, and J. K. Jain, Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene, Nano Lett. 17, 4643 (2017).