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

Area of Science:

• Condensed Matter Physics
• Quantum Hall Effect
• Many-Body Physics

Background:

• The quantum Hall effect in bilayer systems is a complex phenomenon.
• Understanding the behavior of composite fermions is crucial.
• Previous models have limitations in describing interlayer interactions.

Purpose of the Study:

• To introduce and validate a new variational wave function for quantum Hall bilayers.
• To investigate the role of s-wave and p-wave BCS pairing.
• To analyze the crossover physics between large and small layer separations.

Main Methods:

• Development of a novel variational wave function based on s-wave BCS pairing.
• Reexamination of a p-wave BCS pairing trial wave function.
• Exact diagonalization calculations for systems up to 14 electrons.
• Comparison of trial wave functions with ground states over a range of layer separations.

Main Results:

• Excellent agreement between optimized trial wave functions and exact diagonalization results.
• The s-wave wave function naturally accommodates charge imbalance between layers.
• Demonstration of a crossover in physics analogous to the BEC-BCS crossover.
• Validation of the wave function's accuracy across different layer separation regimes.

Conclusions:

• The proposed s-wave BCS pairing wave function is a highly accurate model for quantum Hall bilayers.
• This model provides significant insights into the transition between different physical regimes.
• The findings offer a new perspective on bilayer quantum Hall physics and related phenomena.