Paired composite fermion phase of quantum Hall bilayers at \nu = 1/2 + 1/2

TL;DR

This paper provides numerical evidence for a $p_x + i p_y$ pairing phase of composite fermions in quantum Hall bilayers at half filling, highlighting a transition from a liquid to a paired state as layer spacing varies.

Contribution

It introduces high-accuracy trial wavefunctions for the paired phase and analyzes the competition with a composite fermion liquid at different system sizes and layer spacings.

Findings

Identification of $p_x + i p_y$ pairing in the bilayer system.

Evidence of a phase transition influenced by layer spacing.

Prediction that the pairing phase persists at larger system sizes.

Abstract

We provide numerical evidence for composite fermion pairing in quantum Hall bilayer systems at filling $\nu=1/2 + 1/2$ for intermediate spacing between the layers. We identify the phase as $p_x + i p_y$ pairing, and construct high accuracy trial wavefunctions to describe the groundstate on the sphere. For large distances between the layers, and for finite systems, a competing "Hund's rule" state, or composite fermion liquid, prevails for certain system sizes. We argue that for larger systems, the pairing phase will persist to larger layer spacing.