Pairing and Pair Breaking by Gauge Fluctuations in Bilayer Composite Fermion Metals

TL;DR

This paper investigates how gauge fluctuations influence interlayer pairing of composite fermions in quantum Hall bilayers, revealing a suppressed pairing gap that may explain discrepancies with experimental observations.

Contribution

It introduces a detailed analysis of gauge fluctuation effects on interlayer pairing, highlighting the suppression of the pairing gap and assessing the validity of local approximation methods.

Findings

Pairing gap scales as inverse square of layer spacing when only attractive interactions are considered.

Including repulsive interactions further suppresses the pairing gap, aligning with experimental deviations.

Numerical analysis supports the validity of the local approximation in the studied regime.

Abstract

We study interlayer pairing of composite fermions in the total $\nu=1/2+1/2$ quantum Hall bilayer as a possible framework for understanding the experimentally observed transition from a compressible state at large layer spacing to a bilayer quantum Hall state at small layer spacing. We consider a model in which the effective interlayer composite fermion pairing interaction mediated by the Chern-Simons gauge fields in the two layers is singular with both attractive (out-of-phase) and repulsive (in-phase) components diverging at low frequency. If only the more singular attractive interaction is included the pairing gap obtained by solving the gap equation is proportional to the inverse of the layer spacing squared. In the so-called local approximation, we find that when the less singular repulsive interactions are also included the pairing gap still falls off as inverse layer spacing squared, consistent with recent analyses, but is strongly suppressed to a degree that may account for the fact that this predicted inverse square dependence is not observed experimentally. The analytically obtained local approximation solutions are then used as a starting point to numerically iterate the full gap equation to assess the validity of the approximation in this limit.