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

Abstract

Fascinating structures have arisen from the study of the fractional quantum Hall effect (FQHE) at the even denominator fraction of 5/25/2. We consider the FQHE at another even denominator fraction, namely \nu=2+3/8ν=2+3/8, where a well-developed and quantized Hall plateau has been observed in experiments. We examine the non-Abelian state described by the ``\bar{3}\bar{2}^{2}1^{4}3‾2‾214" parton wave function and numerically demonstrate it to be a feasible candidate for the ground state at \nu=2+3/8ν=2+3/8. We make predictions for experimentally measurable properties of the \bar{3}\bar{2}^{2}1^{4}3‾2‾214 state that can reveal its underlying topological structure.

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

“…To obtain the secondquantized representation of the 321 3 wave function we use the method outlined in Refs. [24,30,43]. Since the 321 3 state is uniform we first evaluate all the total orbital angular momentum L = 0 states for the relevant system and then find the expansion coefficients of the desired wave function on this basis of all the L = 0 states.…”

“…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].…”

“…The pseudopotentials {V m } (V m denotes the energy penalty for placing two particles in the relative angular momentum m state) of CFs [12,[16][17][18][19][20][21] indicate that the residual interaction between two CFs occupying the SΛL in the presence of the filled lowest ΛL (LΛL) is hollow-core like, i.e., the interaction is dominated by a strong repulsion in the m = 3 channel. For comparison, the Coulomb interaction between electrons in the LLL, which stabilizes the 1/5 Laughlin state [22][23][24], is dominated by the hardcore V 1 pseudopotential. Thus, for interactions where V 3 V m ∀m = 3, the case realized for CFs in the SΛL, it is not clear if the 1/5 Laughlin state could be stabilized.…”

Bardeen-Cooper-Schrieffer pairing of composite fermions

“…D > D). This is done to ensure the numerical stability of the solution [90]. Further, in order to improve the conditioning of the matrix φ m r (α) i , we used particle configurations obtained after Monte Carlo thermalization.…”

Prediction of non-Abelian fractional quantum Hall effect at $ν{=}2{+}4/11$

“…One way to understand these states is using the parton theory [11], which generalizes the CF theory, to map the FQHE state of electrons to IQHE states of partons that are fermionic particles carrying fractional charges. Recently, a parton sequence that captures most of the fractions observed in the SLL has been proposed [12][13][14]. In this work, we look at the next unexplored member of this parton sequence which produces a non-Abelian state at ν=4/11.…”