Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers

TL;DR

This paper investigates the pairing symmetry of composite fermions in quantum Hall bilayers, revealing that interlayer paired states with angular momentum l=+1 are energetically favored due to Coulomb and gauge interactions.

Contribution

It provides a detailed analysis of the pairing symmetry using the HLR theory, highlighting the energetic preference for specific angular momentum states in quantum Hall bilayers.

Findings

Interlayer paired states with l=+1 are favored at certain fillings.

Degeneracy between ±l states is lifted by density-current interactions.

Long-range Coulomb and Chern-Simons interactions influence pairing symmetry.

Abstract

We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum $l=+1$ are energetically favored for filling $\nu=\frac{1}{2}+\frac{1}{2}$ and $\frac{1}{4}+\frac{1}{4}$. The degeneracy between states with $\pm l$ is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory.