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

TL;DR

This paper proposes a new variational wavefunction for quantum Hall bilayers at total filling factor 1, based on s-wave pairing of composite fermions, which accurately matches exact ground states and offers insights into interlayer physics.

Contribution

Introduces an s-wave paired composite-fermion wavefunction for quantum Hall bilayers, capturing the crossover from large to small interlayer separation.

Findings

High overlap with exact ground states across all layer separations

Provides a framework for understanding charge imbalance effects

Reveals a BEC-BCS crossover in the bilayer system

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.