Tunneling-driven breakdown of the 331 state and the emergent Pfaffian and composite Fermi liquid phases

TL;DR

This paper investigates how increasing tunneling in quantum Hall bilayers can destroy the 331 state, leading to a transition into a composite Fermi liquid or possibly a critical state with Pfaffian-like properties, using exact diagonalization.

Contribution

It demonstrates that tunneling drives the 331 state into a compressible phase and explores conditions for stabilizing the Pfaffian phase, introducing a two-component BCS model with tunneling constraints.

Findings

Tunneling destroys the 331 state, leading to a composite Fermi liquid.

An intermediate critical state may exhibit properties of the Moore-Read Pfaffian.

Exact diagonalization confirms the phase transition driven by tunneling.

Abstract

We examine the possibility of creating the Moore-Read Pfaffian in the lowest Landau level when the multicomponent Halperin 331 state (believed to describe quantum Hall bilayers and wide quantum wells at the filling factor $\nu=1/2$) is destroyed by the increase of tunneling. Using exact diagonalization of the bilayer Hamiltonian with short-range and long-range (Coulomb) interactions in spherical and periodic rectangular geometries, we establish that tunneling is a perturbation that drives the 331 state into a compressible composite Fermi liquid, with the possibility for an intermediate critical state that possesses some properties of the Moore-Read Pfaffian. These results are interpreted in the two-component BCS model for Cauchy pairing with a tunneling constraint. We comment on the conditions to be imposed on a system with fluctuating density in order to achieve the stable Pfaffian phase.