Fractional Quantum Hall States of the $\mathcal{A}$ phase in the Second Landau Level

TL;DR

This paper proposes a new class of gapped fractional quantum Hall states, called the $ ext{A}$ phase, in the second Landau level, with high overlap with exact ground states and potential non-Abelian quasiparticles, predicting observable thermal Hall conductance.

Contribution

It introduces a unified framework for a sequence of $ ext{A}$ phase states in the second Landau level, with explicit trial wavefunctions and experimental predictions.

Findings

High overlap of trial wavefunctions with exact ground states.

Prediction of non-Abelian quasiparticles with specific charge.

Verifiable thermal Hall conductance for the proposed states.

Abstract

A proposal of the existence of an {\em Anomalous} phase ($\mathcal{A}$ phase) [https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.131.056202 Das et al., Phys. Rev. Lett. 131, 056202 (2023)] at the experimental range of moderate Landau-level-mixing strength has recently been made for $5/2$ state. We here report that the gapped $\mathcal{A}$ phase is generic to the sequence of spin-polarized fractional quantum Hall states with filling fractions $\nu = n/(nm-1)$ and $\nu = 1-n/(nm-1)$, $(n \geqslant 1,\,m\geqslant 3)$, that exhausts almost all the observed states and also predicts some states in the second Landau level for GaAs systems. Our proposed trial wavefunctions for all these states have remarkably high overlaps with the corresponding exact ground states and can support non-Abelian quasiparticle excitations with charge $e/[2(nm-1)]$. By analyzing edge modes, we predict experimentally verifiable thermal Hall conductance $2.5(\pi^2 k_B^2T/3h)$ for all the states in these sequences.