Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers

Abstract

We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum $l=+1$ are energetically favored for filling $\nu =\frac{1}{2}+\frac{1}{2}$ and $\frac{1}{4}+\frac{1}{4}$. The degeneracy between states with $\pm l$ is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory.

20 pages, 11 figures

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• XY* transition and extraordinary boundary criticality from fractional exciton condensation in quantum Hall bilayer
• Deconfined Metal-Insulator Transitions in Quantum Hall Bilayers
• Paired states in half-filled Landau levels
• Pairing of Composite-Electrons and Composite-Holes in ${\nu }_T=1$ Quantum Hall Bilayers
• Exciton Condensation in Quantum Hall Bilayers at Total Filling ${\nu }_T=5$
• Quantum Hall bilayer in dipole representation
• Fate of superconductivity in disordered Dirac and semi-Dirac semimetals
• Single-parameter variational wavefunctions for quantum Hall bilayers
• Successive electron-vortex binding in quantum Hall bilayers at $\nu =\frac{1}{4}+\frac{3}{4}$
• Critical Behavior and Duality in Dimensionally Reduced Planar Chern-Simons Superconductors
• On dualities of paired quantum Hall bilayer states at ${\nu }_T=\frac{1}{2}+\frac{1}{2}$
• Bilayers and quasi-3D stacks of Jain series fractional quantum Hall states from parton construction