Intrinsic Gap of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>5</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math>Fractional Quantum Hall State

Dean, Cory; Piot, B. A.; Hayden, Patrick; Sarma, S. Das; Gervais, G.; Pfeiffer, L. N.; West, K. W.

doi:10.1103/physrevlett.100.146803

Cited by 103 publications

(109 citation statements)

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“…Two important aspects distinguish our work from previous tilted field experiments in the second Landau level (SLL) [13,14,15,16,17]. First, we examine a relatively strong 5 2 -state occurring at lower magnetic field than previously observed (owing to our low density sample [18]) in the non-perturbative Landau level coupling regime where the Coulomb interaction energy is greater than the Landau level separation.Secondly, we study the FQH energy gap in a sample with a relatively wide 2D quantum well so that under tilt the magnetic length associated with B becomes of order or smaller than the well width, allowing us to study the effect of orbital coupling to the parallel field. Comparing the even-denominator 3 , we find that the in-plane magnetic field induces dramatically (and qualitatively) different behaviour in the two activation gaps.…”

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Contrasting Behavior of the52and73Fractional Quantum Hall Effect in a Tilted Field

et al. 2008

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Using a tilted field geometry, the effect of an in-plane magnetic field on the even denominator ν = 5 2 fractional quantum Hall state is studied. The energy gap of the ν = 5 2 state is found to collapse linearly with the in-plane magnetic field above ∼ 0.5T. In contrast, a strong enhancement of the gap is observed for the ν = 7 3 state. The radically distinct tilted-field behaviour between the two states is discussed in terms of Zeeman and magneto-orbital coupling within the context of the proposed Moore-Read Pfaffian wavefunction for the The incompressible even-denominator fractional quantum Hall effect (FQHE) at filling factor ν = 5 2 [1] remains one of the most exotic phenomena ever discovered in condensed matter physics. Of the ∼100 FQH states observed in high-mobility two-dimensional electron gas (2DEG) structures, the 5 2 FQH state continues to represent the only violation of the odd-denominator rule. Aside from the fundamental questions this even-denominator FQH state raises concerning our understanding of strongly correlated electron behaviour, the 5 2 state has received particular attention because of its possible description by the Moore-Read Pfaffian wave function [2], which exhibits non-abelian quantum statistics. This potential non-abelian property makes the 5 2 FQHE a strong candidate for the realization of fault-tolerant topological quantum computation [3]. Recent measurements of the e * = e/4 quasi-particle charge [4], as well as the tunneling spectra [5], are fully consistent with a Moore-Read Pfaffian wavefunction (or its particle-hole conjugate, the so-called anti-Pfaffian [6,7]). However, an unequivocal experimental proof is still lacking, in part due to other possible candidate paired-states, such as the (abelian) Halperin (3,3,1) state, which could in principle be realized at ν = Key features of the Moore-Read Pfaffian that distinguish it from other possible wavefunctions include its fully spin-polarized electron polarization [10,11,12], as well as the non-zero angular momentum of its p x + ıp y pairing, very similar to the A 1 -phase of superfluid 3 He. In this Letter, we investigate the 5 2 FQH spin polarization by measuring the activation energy gap of the 5 2 (and particle-hole conjugate 7 2 ) and neighbouring 7 3 state in a tilted field geometry where, in addition to the perpendicular field (B ⊥ ), a parallel field (B ) is applied in the plane of the 2DEG. Two important aspects distinguish our work from previous tilted field experiments in the second Landau level (SLL) [13,14,15,16,17]. First, we examine a relatively strong 5 2 -state occurring at lower magnetic field than previously observed (owing to our low density sample [18]) in the non-perturbative Landau level coupling regime where the Coulomb interaction energy is greater than the Landau level separation.Secondly, we study the FQH energy gap in a sample with a relatively wide 2D quantum well so that under tilt the magnetic length associated with B becomes of order or smaller than the well width, allowing us to study the effect ...

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“…Treatment with a red LED was used during the cooldown. Details of the sample cooling and temperature measurement have been described elsewhere [18]. The tilted field geometry was achieved by rotating the sample in situ in a static field.…”

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Contrasting Behavior of the52and73Fractional Quantum Hall Effect in a Tilted Field

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“…[35], and Ref. [36]. The two density points at n ~ 4.4  10 10 cm -2 were obtained in Bay 3 at the high B/T facilities of National High Magnetic Field Laboratory in a specimen cut from the same wafer as sample B.…”

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Competing Quantum Hall Phases in the Second Landau Level in Low Density Limit

Pan

Serafin

Xia

et al. 2015

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Abstract:In this Rapid Communication we present the results from two high-quality, low-density GaAs quantum wells. In sample A of electron density n=5.010 10 cm -2 , anisotropic electronic transport behavior was observed at =7/2 in the second Landau level. We believe that the anisotropy is due to the large Landau level mixing effect in this sample. In sample B of density 4.110 10 cm -2 , strong 8/3, 5/2, and 7/3 fractional quantum Hall states were observed. Furthermore, our energy gap data suggest that, similar to the 8/3 state, the 5/2 state may also be spin unpolarized in the low-density limit. The results from both samples show that the strong electron-electron interactions and a large Landau level mixing effect play an import role in the competing ground states in the second Landau level.

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“…The gap ω CF c , obtained by the coincidence method is for ν = 5/3 (and also for ν = 4/3, see below) by a factor of ∼3 larger than the activation gaps. Generally, gaps are overestimated by theory when disorder, LL mixing, and finite thickness correction are neglected [25][26][27][28]. The difference in gap size reflects the different experimental techniques used to extract ω CF c : The fitting of the CF-LL spectrum [red dashed lines in Figs.…”

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Fractional quantum Hall effect in a dilute magnetic semiconductor

Betthausen

Giudici²,

Iankilevitch³

et al. 2014

Phys. Rev. B

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We report the observation of the fractional quantum Hall effect in the lowest Landau level of a two-dimensional electron system (2DES), residing in the diluted magnetic semiconductor Cd 1−x Mn x Te. The presence of magnetic impurities results in a giant Zeeman splitting leading to an unusual ordering of composite fermion Landau levels. In experiment, this results in an unconventional opening and closing of fractional gaps around the filling factor ν = 3/2 as a function of an in-plane magnetic field, i.e., of the Zeeman energy. By including the s-d exchange energy into the composite Landau level spectrum the opening and closing of the gap at filling factor 5/3 can be modeled quantitatively. The widely tunable spin-splitting in a diluted magnetic 2DES provides a means to manipulate fractional states. The fractional quantum Hall effect (FQHE) is a collective high-magnetic field phenomenon, originating from Coulomb repulsion of electrons confined in two dimensions. At certain fractional fillings, ν = p/q, of the Landau levels (LLs) (ν = filling factor, p,q = integers), quantized plateaus in the Hall resistance ρ xy and the vanishing longitudinal resistance ρ xx herald the presence of peculiar electron correlations [1,2]. Here, the electrons condense into a liquidlike ground state that is separated by a gap from the excited states. Most experiments to date have been carried out on GaAsbased systems, being still the cleanest material system with the highest electron mobilities [3]. When the direction of the magnetic field B is tilted, the orbital LL splitting is given by the field component B ⊥ normal to the two-dimensional electron system (2DES) while the total field strength B determines the Zeeman splitting E Z . Early experiments on GaAs revealed that the ν = 4/3, 5/3, and 8/5 states behaved differently upon tilting the sample [4,5]: While the ν = 4/3 and 8/5 states were undergoing a transition from a spinunpolarized state to a polarized one, the ν = 5/3 state was always fully spin polarized.Although the FQHE has been reported in quite a number of different materials [6][7][8][9][10][11][12], the FQHE has never been observed in a diluted magnetic semiconductor in which atoms with magnetic moment (e.g., Mn 2+ ) are placed in a 2DES. Then, the localized spins in the magnetic impurities' d orbitals interact with the correlated electron system via the quantum mechanical s-d exchange interaction, causing giant Zeeman splitting [13] which is tunable in magnitude, sign, and field dependence [14]. The constant αN 0 specifies the s-d exchange strength and is the largest energy scale in the system. It hence has remained unclear whether FQHE states survive in the presence of magnetic impurities. Below we demonstrate that (i) the FQHE indeed exists in magnetic 2DESs and (ii) the opening and closing of gaps in an in-plane field can be described within a modified composite fermion (CF) picture, in which the s-d exchange is taken into account.Let us first recall the CF model which maps the FQHE onto the integer quantum Hall effe...

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Intrinsic Gap of theν=5/2Fractional Quantum Hall State

Cited by 103 publications

References 31 publications

Contrasting Behavior of the52and73Fractional Quantum Hall Effect in a Tilted Field

Contrasting Behavior of the52and73Fractional Quantum Hall Effect in a Tilted Field

Competing Quantum Hall Phases in the Second Landau Level in Low Density Limit

Fractional quantum Hall effect in a dilute magnetic semiconductor

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