The $\nu=1/2$ Quantum Hall Effect and Symmetry Properties of Two-Component Paired Quantum Hall States

TL;DR

This paper explores paired quantum Hall states at specific filling fractions, providing explicit wavefunctions, proposing experiments to distinguish pairing symmetries, and analyzing experimental data to identify the nature of the $ u=1/2$ state.

Contribution

It introduces explicit wavefunctions for paired quantum Hall states at certain filling fractions and discusses experimental methods to determine their pairing symmetry.

Findings

The $ u=1/2$ state in double layer quantum wells is likely a singlet paired state.

Proposed experiments can differentiate between singlet and triplet pairing.

Existing data supports the singlet pairing interpretation over the triplet '3-3-1' state.

Abstract

We describe paired quantum Hall states at filling fractions $\nu$, where $\nu^{-1}$ is an integer, and present explicit wavefunctions for these states. Experiments are proposed to distinguish between paired states of singlet and triplet symmetry. It is argued from existing experimental data that the $\nu=1/2$ state observed in double layer quantum wells is a singlet and not a triplet paired state. In contrast, this state has been interpreted as a `3-3-1 state' which is a triplet paired state.