Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene

Skipping the Odds When confined to a plane and placed in a magnetic field at low temperatures, electrons are separated by energy into the so-called Landau levels; adding an extra electron after a Landau level that has been filled is costly. In some systems, electron-electron interactions cause the appearance of sublevels, in a phenomenon known as the fractional quantum Hall effect (FQHE). This effect has been observed in graphene, but the number of levels that had been resolved was limited. Feldman et al. (p. 1196) directly measured the change in the chemical potential caused by varying electron density, which is controlled by gate voltage. Once the FQH states were identified, the Landau levels with odd-numerator fractional fillings were found to be missing between filling factors 1 and 2, because of the broken and preserved symmetries of graphene. These observations help to explain how the FQHE in graphene is different from that observed in conventional semiconductors, and the technique will also allow local measurements to be made; hence, monitoring of spatial variations in sample behavior is possible. A scanning single-electron transistor is used to measure the local compressibility of graphene’s electronic states. Graphene provides a rich platform to study many-body effects, owing to its massless chiral charge carriers and the fourfold degeneracy arising from their spin and valley degrees of freedom. We use a scanning single-electron transistor to measure the local electronic compressibility of suspended graphene, and we observed an unusual pattern of incompressible fractional quantum Hall states that follows the standard composite fermion sequence between filling factors ν = 0 and 1 but involves only even-numerator fractions between ν = 1 and 2. We further investigated this surprising hierarchy by extracting the corresponding energy gaps as a function of the magnetic field. The sequence and relative strengths of the fractional quantum Hall states provide insight into the interplay between electronic correlations and the inherent symmetries of graphene.