s-Wave Paired Electron and Hole Composite Fermion Trial State for Quantum Hall Bilayers with ν=1

Glenn Wagner; Dung X Nguyen; Steven H Simon; Bertrand I Halperin

doi:10.1103/PhysRevLett.127.246803

s-Wave Paired Electron and Hole Composite Fermion Trial State for Quantum Hall Bilayers with ν=1

Phys Rev Lett. 2021 Dec 10;127(24):246803. doi: 10.1103/PhysRevLett.127.246803.

Authors

Glenn Wagner^{1

2}, Dung X Nguyen³, Steven H Simon¹, Bertrand I Halperin⁴

Affiliations

¹ Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Oxford OX1 3PU, United Kingdom.
² Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
³ Brown Theoretical Physics Center, Brown University, Providence, Rhode Island 02912, USA.
⁴ Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA.

PMID: 34951796
DOI: 10.1103/PhysRevLett.127.246803

Abstract

We introduce a new variational wave function for a quantum Hall bilayer at total filling ν_{T}=1, which is based on s-wave BCS pairing between electron composite fermions in one layer and hole composite fermions in the other. In addition, we reexamine a trial wave function based on p-wave BCS pairing between electron composite fermions in both layers. We compute the overlap of the optimized trial functions 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 s-wave trial wave function 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.