Evidence for a fractional fractal quantum Hall effect in graphene superlattices

Mixing interactions and superlattices Under the influence of an external magnetic field, the energies of electrons in two-dimensional systems group into the so-called Landau levels. In the cleanest samples, interactions among electrons lead to fractional quantum Hall (FQH) states. If such a system is then subjected to a superlattice potential, it is unclear whether the fragile FQH states will survive. To address this question, Wang et al. sandwiched graphene between two layers of hexagonal boron nitride. Transport measurements on the superlattice showed that some FQH states did survive. Furthermore, the interplay between interactions and the superlattice potential produced additional, anomalous states. Science, this issue p. 1231 Transport measurements are used to detect anomalous states in graphene/hexagonal boron nitride heterostructures. The Hofstadter energy spectrum provides a uniquely tunable system to study emergent topological order in the regime of strong interactions. Previous experiments, however, have been limited to low Bloch band fillings where only the Landau level index plays a role. We report measurements of high-mobility graphene superlattices where the complete unit cell of the Hofstadter spectrum is accessible. We observed coexistence of conventional fractional quantum Hall effect (QHE) states together with the integer QHE states associated with the fractal Hofstadter spectrum. At large magnetic field, we observed signatures of another series of states, which appeared at fractional Bloch filling index. These fractional Bloch band QHE states are not anticipated by existing theoretical pictures and point toward a distinct type of many-body state.