The enigma of the $\nu =2+\frac{3}{8}$ fractional quantum Hall effect

Abstract

The fractional quantum Hall effect at $\nu =2+3/8$, which has been definitively observed, is one of the last fractions for which no viable explanation has so far been demonstrated. Our detailed study suggests that it belongs to a new class of of exotic states described by the Bonderson-Slingerland wave function. Its excitations are non-Abelian anyons similar to those of the well studied Pfaffian state at 5/2, but its wave function has a more complex structure. Using the effective edge theory, we make predictions for various measurable quantities that should enable a confirmation of the underlying topological order of this state.

10 pages, published version

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Cited by in corpus (18)

• Fractional charge and fractional statistics in the quantum Hall effects
• Parton construction of a wave function in the anti-Pfaffian phase
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Fractional Quantum Hall Effect at $\nu =2+4/9$
• A non-Abelian parton state for the $\nu =2+3/8$ fractional quantum Hall effect
• A non-Abelian fractional quantum Hall state at $3/7$ filled Landau level
• Abelian parton state for the $\nu =4/11$ fractional quantum Hall effect
• Parton wave function for the fractional quantum Hall effect at $\nu =6/17$
• Nature of the anomalous $4/13$ fractional quantum Hall effect in graphene
• Prediction of non-Abelian fractional quantum Hall effect at $\nu =2+\frac{4}{11}$
• Modeling free anyons at the bosonic and fermionic ends
• Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level
• Hetero-Orbital Two-Component Fractional Quantum Hall States in Bilayer Graphene
• Bubble phase at $\nu =1/3$ for a spinless hollow-core interaction
• Interplay of superconducting, metallic, and crystalline states of composite fermions at $\nu =1/6$ in wide quantum wells
• Infinite energy solutions to vortex equations governing the fractional quantum Hall effect
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• An indefinite system of equations governing the fractional quantum Hall effect