Robust fractional quantum Hall effect and composite fermions in the $N=2$ Landau level in bilayer graphene

Abstract

The fractional quantum Hall (FQH) effect is a canonical example of electron-electron interactions producing new ground states in many-body systems. Most FQH studies have focused on the lowest Landau level (LL), whose fractional states are successfully explained by the composite fermion (CF) model, in which an even number of magnetic flux quanta are attached to an electron and where states form the sequence of filling factors $\nu =p/(2mp\pm 1)$, with $m$ and $p$ positive integers. In the widely-studied GaAs-based system, the CF picture is thought to become unstable for the $N\ge 2$ LL, where larger residual interactions between CFs are predicted and competing many-body phases have been observed. Here we report transport measurements of FQH states in the $N=2$ LL (filling factors $4<\nu <8$) in bilayer graphene, a system with spin and valley degrees of freedom in all LLs, and an additional orbital degeneracy in the 8-fold degenerate $N=0$/$N=1$ LLs. In contrast with recent observations of particle-hole asymmetry in the $N=0$/$N=1$ LLs of bilayer graphene, the FQH states we observe in the $N=2$ LL are consistent with the CF model: within a LL, they form a complete sequence of particle-hole symmetric states whose relative strength is dependent on their denominators. The FQH states in the $N=2$ LL display energy gaps of a few Kelvin, comparable to and in some cases larger than those of fractional states in the $N=0$/$N=1$ LLs. The FQH states we observe form, to the best of our knowledge, the highest set of particle-hole symmetric pairs seen in any material system.

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Cited by in corpus (16)

• Non-Abelian Parton Fractional Quantum Hall Effect in Multilayer Graphene
• Quantitative transport measurements of fractional quantum Hall energy gaps in edgeless graphene devices
• Effective Landau Level Diagram of Bilayer Graphene
• Imaging anyons with scanning tunneling microscopy
• Fractional quantum Hall effect with unconventional pairing in monolayer graphene
• High-Resolution Tunneling Spectroscopy of Fractional Quantum Hall States
• Application of path-integral quantization to indistinguishable particle systems topologically confined by a magnetic field
• Landau quantization of multilayer graphene on a Haldane sphere
• Local density of states and particle entanglement in topological quantum fluids
• Competition between fractional quantum Hall liquid and electron solid phases in the Landau levels of multilayer graphene
• Forbidden trajectories for path integrals
• Two-component parton fractional quantum Hall state in graphene
• Enhancement in tunneling density of states in Luttinger liquid -- role of non-local interaction
• Topological correlations and breaking of fermionic antisymmetry of electrons in FQHE
• Dipole representation of composite fermions in graphene quantum Hall systems
• Topological states in double monolayer graphene