Correlation-hole induced paired quantum Hall states in lowest Landau level

TL;DR

This paper develops a theory for paired fractional quantum Hall states in the lowest Landau level, revealing how electron-vortex binding leads to various paired states and matching recent experimental observations.

Contribution

It introduces a new theoretical framework describing pairing mechanisms and resulting states in the fractional quantum Hall effect at the lowest Landau level.

Findings

Ground state is Moore-Read Pfaffian for weak interactions

Identifies a new oscillatory pairing Pfaffian at intermediate interactions

Predicts a transition to a Read-Rezayi Fermi liquid at strong interactions

Abstract

A theory is developed for the paired even-denominator fractional quantum Hall states in the lowest Landau level. We show that electrons bind to quantized vortices to form composite fermions, interacting through an exact instantaneous interaction that favors chiral p-wave pairing. Two canonically dual pairing gap functions are related by the bosonic Laughlin wavefunction (Jastraw factor) due to the correlation holes. We find that the ground state is the Moore-Read pfaffian in the long wavelength limit for weak Coulomb interactions, a new pfaffian of an oscillatory pairing function for intermediate interactions, and a Read-Rezayi composite Fermi liquid beyond a critical interaction strength. Our findings are consistent with recent experimental observations of the 1/2 and 1/4 fractional quantum Hall effects in asymmetric wide quantum wells.