Pairing in half-filled Landau level

Abstract

Pairing of composite fermions in half-filled Landau level state is reexamined by solving the BCS gap equation with full frequency dependent current-current interactions. Our results show that there can be a \emph{continuous} transition from the Halperin-Lee-Read state to a chiral odd angular momentum Cooper pair state for short-range contact interaction. This is at odds with the previously established conclusion of first order pairing transition, in which the low frequency effective interaction was assumed for the entire frequency range. We find that even if the low frequency effective interaction is repulsive, it is compensated by the high frequency regime, which is attractive. We construct the phase diagrams and show that $\ell =1$ angular momentum channel is quite different from higher angular momenta $\ell \ge 3$. Remarkably, the full frequency dependent analysis applied to the bilayer Hall system with a total filling fraction $\nu =\frac{1}{2}+\frac{1}{2}$ is quantitatively changed from the previously established results but not qualitatively.

9 pages,7 figures

References in corpus (9)

• Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries, and the fractional quantum Hall effect
• Superconductivity by long-range color magnetic interaction in high-density quark matter
• Non-Fermi Liquid Fixed Point in 2+1 Dimensions
• Gauge Fields and Pairing in Double-Layer Composite Fermion Metals
• Compressible Phase of a Double-Layer Electron System with Total Landau-Level Filling Factor One-Half
• Singular Pair Breaking in the Composite Fermi Liquid Description of the Half-Filled Landau Level
• Interlayer coherent composite Fermi liquid phase in quantum Hall bilayers
• Higher angular momentum pairing from transverse gauge interactions
• Gauge Fluctuations and Interlayer Coherence in Bilayer Composite Fermion Metals

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