Theory of Fractional Quantum Hall States of the \(\mathcal{A}\)-phase in the Second Landau Level

Abstract

A proposal of the existence of an {\em Anomalous} phase (\(\mathcal{A}\)-phase) 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 \(\nu = 1-n/(nm-1)\), \((n \geqslant 1,\,m\geqslant 3)\), thereby predicting several other states in addition to the observed ones in the second Landau level for GaAs systems. Our proposed trial wave functions 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.