Cooper Instability of Composite Fermions

Abstract

When confined to two dimensions and exposed to a strong magnetic field, electrons screen the Coulomb interaction in a topological fashion; they capture and even number of quantum vortices and transform into particl es called `composite fermions'. The fractional quantum Hall effect occurs in such a system when the ratio (or `filling factor', $\nu$) of the number of electrons and the degeneracy of their spin-split energy states (the Landau levels) takes on particular values. The Landau level filling $\nu =1/2$ corresponds to a metallic state in which the composite fermions form a gapless Fermi sea. But for $\nu =5/2$, a fractional quantum Hall effect is observed instead; this unexpected result is the subject of considerable debate and controversy. Here we investigate the difference between these states by considering the theoretical problem of two composite fermions on top of a fully polarized Fermi sea of composite fermions. We find that they undergo Cooper pairing to form a p-wave bound state at $\nu =5/2$, but not at $\nu =1/2$. In effect, the repulsive Coulomb interaction between electrons is overscr eened in the $\nu =5/2$ state by the formation of composite fermions, resulting in a weak, attractive interaction.

12 pages, 3 figures

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• Orbital Landau level dependence of the fractional quantum Hall effect in quasi-two dimensional electron layers: finite-thickness effects
• Competition between quantum-liquid and electron-solid phases in intermediate Landau levels
• Observation of a Fractional Quantum Hall State at $\nu =1/4$ in a Wide GaAs Quantum Well
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• Recent Experimental Progress of Fractional Quantum Hall Effect: 5/2 Filling State and Graphene
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• Evidence for the Collective Nature of the Reentrant Integer Quantum Hall States of the Second Landau Level
• Phase Diagram of Bilayer Composite Fermion States
• Experimental Evidence for a Spin-Polarized Ground State in the ν=5/2 Fractional Quantum Hall Effect
• Paired fractional quantum Hall states and the nu=5/2 puzzle
• Quantum Hall Phase Diagram of Second Landau-level Half-filled Bilayers: Abelian versus Non-Abelian States
• Possible Pairing-Induced Even-Denominator Fractional Quantum Hall Effect in the Lowest Landau Level
• Quantum Hall Phase Diagram of Half-filled Bilayers in the Lowest and the Second Orbital Landau Levels: Abelian versus Non-Abelian Incompressible Fractional Quantum Hall States
• Tilt Induced Localization and Delocalization in the Second Landau Level
• Beyond the Fermi Liquid Paradigm: Hidden Fermi Liquids
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• Possible Anti-Pfaffian Pairing of Composite Fermions in the Lowest Landau Level
• Fermi hypernetted-chain study of half-filled Landau levels with broken rotational symmetry
• Understanding the 5/2 Fractional Quantum Hall Effect without the Pfaffian Wave Function
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• Fractional Quantum Hall Effect in the Second Landau Level: the Importance of Inter-Composite-Fermion Interaction
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• Electron-Electron Interactions and the Paired-to-Nematic Quantum Phase Transition in the Second Landau Level
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• Possible realization of a chiral p-wave paired state in a two component system
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• Onset of Quantum Criticality in the Topological-to-Nematic Transition in a Two-dimensional Electron Gas at Filling Factor $\nu =5/2$
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• Incompressible States of the Interacting Composite Fermions in Negative Effective Magnetic Fields at $\nu =4/13$, 5/17, and 3/10
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• An Anomalous Reentrant 5/2 Quantum Hall Phase at Moderate Landau-Level-Mixing Strength
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• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
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• Numerical studies of the Pfaffian model of the nu=5/2 fractional quantum Hall effect
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• Jastrow-Correlated Wavefunctions for Flat-Band Lattices
• Correlated double-electron additions at the edge of a two-dimensional electronic system
• Identification of topological order in the fractional quantum Hall state at $\nu =1/4$
• In-plane electric fields and the $\nu =\frac{5}{2}$ fractional quantum Hall effect in a disk geometry
• Numerical study of spin quantum Hall transitions in superconductors with broken time-reversal symmetry
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
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• Partial Wave Analysis of Scattering with Nonlocal Aharonov-Bohm Effect and Anomalous Cross Section induced by Quantum Interference
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