The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

Abstract

The Pfaffian phase of electrons in the proximity of a half-filled Landau level is understood to be a p+ip superconductor of composite fermions. We consider the properties of this paired quantum Hall phase when the pairing scale is small, i.e. in the weak-coupling, BCS, limit, where the coherence length is much larger than the charge screening length. We find that, as in a Type I superconductor, the vortices attract so that, upon varying the magnetic field from its magic value at ν=5/2, the system exhibits Coulomb frustrated phase separation. We propose that the weakly and strongly coupled Pfaffian states exemplify a general dichotomy between Type I and Type II quantum Hall fluids.

4 pages, 1 figure

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• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Onset of Quantum Criticality in the Topological-to-Nematic Transition in a Two-dimensional Electron Gas at Filling Factor $\nu =5/2$
• Pair-Density-Wave Order and Paired Fractional Quantum Hall Fluids
• A Typology for Quantum Hall Liquids
• Intertwined Order in Fractional Chern Insulators from Finite-Momentum Pairing of Composite Fermions
• Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas
• Dipolar bogolons: from superfluids to Pfaffians
• Molecular anyons in fractional quantum Hall effect