Gauge Fields and Pairing in Double-Layer Composite Fermion Metals

TL;DR

This paper investigates how out-of-phase gauge fluctuations induce pairing in double-layer composite fermion systems, leading to a quantum Hall state with a gap that depends on layer spacing, revealing the interplay of gauge interactions and pairing.

Contribution

It demonstrates that out-of-phase gauge fluctuations cause pairing in double-layer composite fermion metals, resulting in a quantum Hall state with a gap scaling as 1/d^2, a novel insight into gauge-mediated pairing.

Findings

Out-of-phase gauge fluctuations mediate attractive pairing between composite fermions.

The pairing gap scales as 1/d^2, indicating stronger pairing at smaller layer spacing.

In-phase gauge fluctuations suppress but do not prevent pairing.

Abstract

A symmetrically doped double layer electron system with total filling fraction $\nu=1/m$ decouples into two even denominator ($\nu=1/2 m$) composite fermion `metals' when the layer spacing is large. Out-of-phase fluctuations of the statistical gauge fields in this system mediate a singular attractive pairing interaction between composite fermions in different layers. A strong-coupling analysis shows that for any layer spacing $d$ this pairing interaction leads to the formation of a paired quantum Hall state with a zero-temperature gap $\Delta(0) \propto 1/d^2$. The less singular in-phase gauge fluctuations suppress the size of the zero-temperature gap, $\Delta(0) \propto 1/\left({d^2}{(\ln d)^6}\right)$, but do not eliminate the instability.