Superconducting Order Parameter for the Even-denominator Fractional Quantum Hall Effect

Abstract

One of the most intriguing phenomena in nature is the fractional quantum Hall effect (FQHE) observed in the half-filled second Landau level which, arising in even-denominator filling factors, $\nu =5/2$ and $7/2$, is completely different from other FQHEs in its origin, all of which, except for those two filling factors, occur in odd-denominator fractions. Usually formulated in terms of a trial wave function called the Moore-Read Pfaffian wave function, current leading theories attribute the origin of the 5/2 FQHE to the formation of Cooper pairs, not of electron, but of the true quasi-particle of the system known as composite fermion. The nature of superconductivity resulting from such Cooper pairing is particularly puzzling in the sense that it apparently coexists with strong magnetic fields, which poses an interesting dilemma since the Meissner effect is {\it the} most important defining property of superconductivity. This apparent dilemma is resolved by the fact that composite fermions do not respond to external magnetic field at even-denominator filling factors. To provide direct evidence that it is composite fermions that actually form the superconducting condensate, here, we develop a numerically exact method of creating a Cooper pair of composite fermions and explicitly compute the superconducting order parameter as a function of real space coordinates. As results, in addition to direct evidence for superconductivity, we obtain quantitative predictions for superconducting coherence length. Obtaining such theoretical predictions can serve as an important step toward fault-tolerant topological quantum computation.

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• Non-abelian statistics of half-quantum vortices in p-wave superconductors
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• The Fractional Quantum Hall state at nu=5/2 and the Moore-Read Pfaffian
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• Cooper Instability of Composite Fermions
• Stability and effective masses of composite-fermions in the first and second Landau Level
• Spontaneous Particle-Hole Symmetry Breaking in the $\nu =5/2$ Fractional Quantum Hall Effect

Cited by in corpus (15)

• Landau Level Mixing and the Fractional Quantum Hall Effect
• Competing states for the fractional quantum Hall effect in the 1/3-filled second Landau level
• Evidence for the Collective Nature of the Reentrant Integer Quantum Hall States of the Second Landau Level
• Unpaired composite fermion, topological exciton, and zero mode
• Quantum Phase Transitions and the ν=5/2 Fractional Hall State in Wide Quantum Wells
• Numerical Calculation of the Neutral Fermion Gap at $\nu =5/2$
• The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid
• Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing
• Onset of Quantum Criticality in the Topological-to-Nematic Transition in a Two-dimensional Electron Gas at Filling Factor $\nu =5/2$
• Topological exciton Fermi surfaces in two-component fractional quantized Hall insulators
• Nematic fluctuations balancing the zoo of phases in half-filled quantum Hall systems
• A Particle-Hole-Symmetric Model for a Paired Fractional Quantum Hall State in a Half-filled Landau Level
• Competition of Pairing and Nematicity in the Two-Dimensional Electron Gas
• Fractional quantum Hall effect at the filling factor $\nu =5/2$
• Exploring Quantum Hall Physics at Ultra-Low Temperatures and at High Pressures