Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene (1201.5128v1)

Abstract: Interactions among electrons can give rise to striking collective phenomena when the kinetic energy of charge carriers is suppressed. One example is the fractional quantum Hall effect, in which correlations between electrons moving in two dimensions under the influence of a strong magnetic field generate excitations with fractional charge. Graphene provides a platform to study unique many-body effects due to its massless chiral charge carriers and the fourfold degeneracy that arises from their spin and valley degrees of freedom. Here we report local electronic compressibility measurements of a suspended graphene flake performed using a scanning single-electron transistor. Between Landau level filling v = 0 and 1, we observe incompressible fractional quantum Hall states that follow the standard composite fermion sequence v = p/(2p \pm 1) for all integer p \leq 4. In contrast, incompressible behavior occurs only at v = 4/3, 8/5, 10/7 and 14/9 between v = 1 and 2. These fractions correspond to a subset of the standard composite fermion sequence involving only even numerators, suggesting a robust underlying symmetry. We extract the energy gaps associated with each fractional quantum Hall state as a function of magnetic field. The states at v = 1/3, 2/3, 4/3 and 8/5 are the strongest at low field, and persist below 1.5 T. The unusual sequence of incompressible states provides insight into the interplay between electronic correlations and SU(4) symmetry in graphene.

Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene: An Analytical Overview

The paper "Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene" explores the emergent fractional quantum Hall effect (FQHE) in graphene under a strong perpendicular magnetic field using local electronic compressibility measurements via a scanning single-electron transistor. The paper undertaken by Feldman, Krauss, Smet, and Yacoby offers significant insights into the behavior of Dirac fermions in graphene, elucidating the impact of SU(4) symmetry on quantum Hall states.

Key Findings

The research identifies the occurrence of incompressible fractional quantum Hall states in suspended graphene, diverging from sequences traditionally observed in GaAs systems. This divergence is prominently evident between the Landau level filling factors $\nu = 1$ and $\nu = 2$, where only states with even numerators such as $\nu = 4/3$, $\nu = 8/5$, $\nu = 10/7$, and $\nu = 14/9$ manifest. This unique sequence is hypothesized as indicative of strong SU(2) or SU(4) symmetry influences within graphene.

Numerical Results and Implications

Through compressibility measurements, the energy gaps associated with the fractional quantum Hall states exhibit behavior notably distinct from theoretical predictions. The strongest states persist at low magnetic fields below 1.5 T, with the sequence $\nu = 1/3$, $\nu = 2/3$, $\nu = 4/3$, and $\nu = 8/5$ demonstrating conspicuous robustness and revealing larger gap sizes than previously predicted by theory. In suspended graphene, the extracted energy gaps are comparable to activation studies, indicating possible sample disorder as a contributing factor to smaller-than-expected gaps.

Theoretical and Practical Implications

The findings present intriguing theoretical implications for the understanding of interaction-driven phenomena in Dirac systems. The alignment of incompressible states with SU(4) symmetry opens new avenues for exploring exotic fractional quantum Hall effects unique to graphene. Furthermore, the robustness of specific states under varying magnetic fields suggests potential applications in quantum computing and novel electronic devices requiring stable quantum coherence.

Future Directions

This paper sets the stage for further exploration into the symmetries inherent in graphene's electronic structure and the conditions enhancing or suppressing fractional quantum Hall states. Future research could deepen understanding of quasiparticle interactions and their influence on electronic compressibility, paving the way for advances in material science applications. Additionally, refinement in sample preparation techniques aiming at reducing disorder could yield more pronounced observations aligning experimental results closer to theoretical models.

In summary, the research offers a solid framework for dissecting the unconventional fractional quantum Hall sequences in graphene and delineates the intriguing role of SU(4) symmetry, positioning graphene as a frontier material in quantum Hall physics.