Non-Abelian fractional quantum Hall state at 3/7 -filled Landau level

Abstract

We consider a non-Abelian candidate state at filling factor ν = 3/7 state belonging to the parton family. We find that, in the second Landau level of GaAs (i.e., at filling factor ν = 2 + 3/7), this state is energetically superior to the standard Jain composite-fermion state and also provides a very good representation of the ground state found in exact diagonalization studies of finite systems. This leads us to predict that if a fractional quantum Hall effect is observed at ν = 3/7 in the second Landau level, it is likely to be described by this new non-Abelian state. We enumerate experimentally measurable properties that can verify the topological structure of this state.

Abelian topological order of ν=2/5 and 3/7 fractional quantum Hall states in lattice models

“…Since an increase in L y /l B coarsely corresponds to an increase in L y , this is an effect that was not apparent in the previous two states. In line with the observed trend, we obtain a topological entanglement entropy of γ = 1.020 ± 0.353, which is in agreement with the Abelian 075132-4 theory value of γ = ln( √ 7) ≈ 0.973 and well separated from the non-Abelian prediction of γ = ln( 7(ϕ 2 + 1)) ≈ 1.616 [51][52][53][54]. The derivation of the total quantum dimensions is discussed in Appendix C.…”

A non-Abelian parton state for the $ν=2+3/8$ fractional quantum Hall effect

“…• The3 2 1 3 state at 3/7 was considered in Ref. [2] and was shown to be feasible at and in the vicinity of the SLL (see also Appendix C where we show new results that further support the viability of the3 2 1 3 state in the SLL). Although FQHE has not been established at ν = 2 + 3/7, some signatures of it have been reported [14].…”

“…The3 2 1 3 state has been proposed as a candidate [2] to describe an FQHE that could arise at ν = 2+3/7. As yet, FQHE has not been definitely established at 3/7 in the second Landau level, though signatures of it have been seen in experiments [14].…”

“…To calculate the charge gap, we use Eq. (1) with n q = 3 since the insertion of a single flux quantum in the3 2 1 3 state produces three fundamental quasiholes each of charge e/7 [2]. The neutral and charge gaps for N = 12, evaluated using exact diagonalization with both the spherical and disk pseudopotentials, are about 0.015 e 2 /(ε ) and 0.001 e 2 /(ε ) respectively at width, w = 0 and decrease with increasing w as shown in Fig.…”

Fractional quantum Hall effect at ν=2+4/9

“…The Jain states, described by the wave function Ψ Jain ν=n/(2pn±1) = P LLL Φ ±n Φ 2p 1 , can be re-interpreted as (2p + 1)-parton states where 2p partons form a ν = 1 IQHE state and one parton forms a ν = ±n IQHE state. Numerous parton states, beyond the Laughlin and Jain states, have been proposed as promising candidates to describe FQHE states occurring in the SΛL [28], second LL (SLL) [30][31][32][33][34], wide quantum wells [35], and in the LLs of graphene [24,[36][37][38][39][40]. These works suggest that it is plausible that viable candidate parton states can be constructed to capture all the observed FQHE states [24,32].…”