Topological d-wave pairing structures in Jain states

TL;DR

This paper explores d-wave topological pairing in Jain states, revealing connections to neutral fermions, the Haldane-Rezayi state, and extending the analysis to polarized and integer quantum Hall states.

Contribution

It introduces a pairing form for Jain spin singlet states, identifies their connection with neutral excitations, and extends topological pairing analysis to polarized and integer quantum Hall states.

Findings

Recognition of d-wave weak pairing of neutral fermions in Jain states

High overlaps with Jain spin singlet state away from hollow core model

Extension of topological pairing analysis to polarized and integer quantum Hall states

Abstract

We discuss d-wave topological (broken time reversal symmetry) pairing structures in unpolarized and polarized Jain states. We demonstrate pairing in the Jain spin singlet state by rewriting it in an explicit pairing form, in which we can recognize d-wave weak pairing of underlying quasiparticles - neutral fermions. We find and describe the root configuration of the Jain spin singlet state and its connection with neutral excitations of the Haldane-Rezayi state, and study the transition between these states via exact diagonalization. We find high overlaps with the Jain spin singlet state upon a departure from the hollow core model for which the Haldane-Rezayi state is the exact ground state. Due to a proven algebraic identity we were able to extend the analysis of topological d-wave pairing structures to polarized Jain states and integer quantum Hall states, and discuss its consequences.