$s$-wave paired composite-fermion electron-hole trial state for quantum Hall bilayers with $\nu =1$

Abstract

We introduce a new variational wavefunction for a quantum Hall bilayer at total filling $\nu =1$, which is based on $s$-wave BCS pairing between composite-fermion electrons in one layer and composite-fermion holes in the other. We compute the overlap of the optimized trial function with the ground state from exact diagonalization calculations of up to 14 electrons in a spherical geometry, and we find excellent agreement over the entire range of values of the ratio between the layer separation and the magnetic length. The trial wavefunction naturally allows for charge imbalance between the layers and provides important insights into how the physics at large interlayer separations crosses over to that at small separations in a fashion analogous to the BEC-BCS crossover.

arXiv comment18 pages, 8 figures

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• Electrical Control of Two-Dimensional Electron-Hole Fluids in the Quantum Hall Regime
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• Pairing of Composite-Electrons and Composite-Holes in ${\nu }_T=1$ Quantum Hall Bilayers
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• Successive electron-vortex binding in quantum Hall bilayers at $\nu =\frac{1}{4}+\frac{3}{4}$
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• Variational wavefunctions for fractional topological insulators
• Two-fluid theory of composite bosons and fermions and the quantum Hall proximity effect