Beyond fractional quantum Hall
Unlike most electronic topological phenomena, the fractional quantum Hall effect requires correlations among electrons. Spanton et al. describe a class of related but even more unusual states, the fractional Chern insulators (see the Perspective by Repellin and Regnault). They observed these states in samples of bilayer graphene, where one of the graphene layers was misaligned by a small angle with respect to an adjoining layer of hexagonal boron nitride. The misalignment created a superlattice potential and topologically nontrivial bands, which had a fractional filling, thanks to strong electronic interactions. The findings expand the class of correlated topological states, which have been predicted to harbor exotic excitations.
Abstract
Topologically ordered phases are characterized by long-range quantum entanglement and fractional statistics rather than by symmetry breaking. First observed in a fractionally filled continuum Landau level, topological order has since been proposed to arise more generally at fractional fillings of topologically nontrivial Chern bands. Here we report the observation of gapped states at fractional fillings of Harper-Hofstadter bands arising from the interplay of a magnetic field and a superlattice potential in a bilayer graphene–hexagonal boron nitride heterostructure. We observed phases at fractional filling of bands with Chern indices 
. Some of these phases, in 
and 
bands, are characterized by fractional Hall conductance—that is, they are known as fractional Chern insulators and constitute an example of topological order beyond Landau levels.
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