Enigmatic<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>4</mml:mn><mml:mo>/</mml:mo><mml:mn>11</mml:mn></mml:mrow></mml:math>State: A Prototype for Unconventional Fractional Quantum Hall Effect

Mukherjee, Sampad; Mandal, Sudhansu S.; Wu, Ying-Hai; Wójs, Arkadiusz; Jain, J. K.

doi:10.1103/physrevlett.112.016801

Cited by 49 publications

(45 citation statements)

References 48 publications

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“…A good qualitative and semiquantitative theoretical understanding of these transitions has been obtained in terms of integer or fractional quantum Hall effect of spinful composite fermions 8,44,47,[57][58][59][60][61][62][63][64][65] , which successfully predicts the allowed spin polarizations at all of these filling factors and also provides an estimate of the the critical Zeeman energy where transitions between them occur. While these quantitative estimates are a good zeroth order approximation, their accuracy has not been carefully evaluated in the past.…”

Section: Phase Diagram Of Spinful Cf Statesmentioning

confidence: 99%

Fractional quantum Hall effect in graphene: Quantitative comparison between theory and experiment

et al. 2015

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The observation of extensive fractional quantum Hall states in graphene brings out the possibility of more accurate quantitative comparisons between theory and experiment than previously possible, because of the negligibility of finite width corrections. We obtain accurate phase diagram for differently spin-polarized fractional quantum Hall states, and also estimate the effect of Landau level mixing using the modified interaction pseudopotentials given in the literature. We find that the observed phase diagram is in good quantitative agreement with theory that neglects Landau level mixing, but the agreement becomes significantly worse when Landau level mixing is incorporated assuming that the corrections to the energies are linear in the Landau level mixing parameter λ. This implies that a first order perturbation theory in λ is inadequate for the current experimental systems, for which λ is typically on the order of or greater than one. We also test the accuracy of the composite-fermion theory and find that it is very accurate for the states of the form n/(2n + 1) but for the states at n/(2n − 1) the results are sensitive to the lowest Landau level projection method. An earlier prediction of an absence of spin transitions for the n/(4n + 1) states is confirmed by more rigorous calculations, and new predictions are made regarding spin physics for the n/(4n − 1) states.

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Section: Phase Diagram Of Spinful Cf Statesmentioning

confidence: 99%

Fractional quantum Hall effect in graphene: Quantitative comparison between theory and experiment

et al. 2015

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“…The spectra of partially polarized and fully polarized 4/11 states have been discussed previously in Refs. 47,48,50,51,75 . The 4/11 FQHE has been observed but no spin phase transition has yet been observed.…”

Section: Appendix E Spin-singlet Fqhe At 4/11mentioning

confidence: 99%

“…at 4/11, 5/13, were observed by Pan et al 46 . These motivated theoretical studies of FQHE of fully spin polarized composite fermions 47,48 as well as partially spin polarized FQHE of composite fermions [49][50][51] . The spin polarization of these states has not been measured experimentally so far, however.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of fractional quantum Hall effect of composite fermions in multicomponent systems

et al. 2015

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While the integer quantum Hall effect of composite fermions manifests as the prominent fractional quantum Hall effect (FQHE) of electrons, the FQHE of composite fermions produces further, more delicate states, arising from a weak residual interaction between composite fermions. We study the spin phase diagram of these states, motivated by the recent experimental observation by Liu et al. [Phys. Rev. Lett. 113, 246803 (2014) and private communication] of several spin-polarization transitions at 4/5, 5/7, 6/5, 9/7, 7/9, 8/11 and 10/13 in GaAs systems. We show that the FQHE of composite fermions is much more prevalent in multicomponent systems, and consider the feasibility of such states for systems with N components for an SU(N ) symmetric interaction. Our results apply to GaAs quantum wells, wherein electrons have two components, to AlAs quantum wells and graphene, wherein electrons have four components (two spins and two valleys), and to an Hterminated Si(111) surface, which can have six components. The aim of this article is to provide a fairly comprehensive list of possible incompressible fractional quantum Hall states of composite fermions, their SU(N ) spin content, their energies, and their phase diagram as a function of the generalized "Zeeman" energy. We obtain results at three levels of approximation: from ground state wave functions of the composite fermion theory, from composite fermion diagonalization, and, whenever possible, from exact diagonalization. Effects of finite quantum well thickness and Landau level mixing are neglected in this study. We compare our theoretical results with the experiments of Liu et al. [Phys. Rev. Lett. 113, 246803 (2014)

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“…It has been proposed that the enigmatic FQHSs observed at ν = 4/11 and 5/13 in the highest quality samples can be interpreted as the FQHSs of interacting 2 CFs at ν CF = +4/3 and +5/3 [5,6]. A recent theoretical study predicts a transition of the ν = 4/11 FQHS to full spin polarization when E Z /V C is about 0.025 [21]. Our observed transition of the ν = 4/5 (ν CF = −4/3) FQHS appears at E Z /V C 0.015 to 0.024, in different QWs with well width ranging from 65 to 31 nm and corresponding λ/l B 1.7 to 1.1 [10], consistent with this theoretically predicted value.…”

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Fractional Quantum Hall Effect and Wigner Crystal of Interacting Composite Fermions

et al. 2014

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In two-dimensional electron systems confined to GaAs quantum wells, as a function of either tilting the sample in magnetic field or increasing density, we observe multiple transitions of the fractional quantum Hall states (FQHSs) near filling factors ν = 3/4 and 5/4. The data reveal that these are spin-polarization transitions of interacting two-flux composite Fermions, which form their own FQHSs at these fillings. The fact that the reentrant integer quantum Hall effect near ν = 4/5 always develops following the transition to full spin polarization of the ν = 4/5 FQHS strongly links the reentrant phase to a pinned ferromagnetic Wigner crystal of two-flux composite Fermions.Fractional quantum Hall states (FQHSs) are among the most fundamental hallmarks of ultra-clean interacting two-dimensional electron systems (2DESs) at a large perpendicular magnetic field (B ⊥ ) [1]. These incompressible quantum liquid phases, signaled by the vanishing of the longitudinal resistance (R xx ) and the quantization of the Hall resistance (R xy ), can be explained by mapping the interacting electrons to a system of essentially noninteracting, 2p-flux composite Fermions ( 2p CFs), each formed by attaching 2p magnetic flux quanta to an electron (p is an integer). The 2p CFs have discrete energy levels, the so-called Λ-levels, and the FQHSs of electrons seen around Landau level (LL) filling factor ν = 1/2 (1/4) would correspond to the integer quantum Hall states of 2 CFs (. In state-of-the-art, highmobility 2DESs, FQHSs also develop around ν = 3/4, and are usually understood as the particle-hole counterparts of the FQHSs near ν = 1/4 through the relation. Alternatively, these states might also be the FQHSs of interacting 2 CFs at ν CF = ν/(1 − 2ν). For example, the ν = 4/5 state is the ν CF = −4/3 FQHS of 2p CFs, and has the same origin as the unconventional FQHS seen at ν = 4/11 (ν CF = 4/3) [5,6].Another hallmark of clean 2DESs is an insulating phase that terminates the series of FQHSs at low fillings, near ν = 1/5, [7,8]. This insulating phase is generally believed to be an electron Wigner crystal, pinned by the small but ubiquitous disorder potential [9]. Recently, an insulating phase was observed near ν = 4/5 in clean 2DESs [10,11]. This phase, which is signaled by a reentrant integer quantum Hall state (RIQHS) near ν = 1, was interpreted as the particle-hole symmetric state of the Wigner crystal seen at very small ν [10,11]. In this picture, the holes, unoccupied states in the lowest LL, have filling factor ν h ∼ 1/5 (= 1 − 4/5) and form a liquid phase when the short-range interaction is strong; see the left panel of Fig. 1(a). They turn into a solid phase when the thickness of the 2DES increases and the long-range interaction dominates (right panel of Fig. 1(a)). This interpretation is plausible, since the RIQHS only appears when the well-width (W ) is more than five times larger than the magnetic length. However, it does not predict or allow for any transitions of the ν = 4/5 FQHS, which is always seen just before the RIQHS de...

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Enigmatic4/11State: A Prototype for Unconventional Fractional Quantum Hall Effect

Cited by 49 publications

References 48 publications

Fractional quantum Hall effect in graphene: Quantitative comparison between theory and experiment

Fractional quantum Hall effect in graphene: Quantitative comparison between theory and experiment

Phase diagram of fractional quantum Hall effect of composite fermions in multicomponent systems

Fractional Quantum Hall Effect and Wigner Crystal of Interacting Composite Fermions

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