Composite Fermion Theory of Exotic Fractional Quantum Hall Effect

Jain, J. K.

doi:10.1146/annurev-conmatphys-031214-014606

Cited by 38 publications

(39 citation statements)

References 150 publications

(175 reference statements)

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“…For example, for 2/5 and 2/3, which both map into n = 2 of composite fermions, we have a fully spin polarized state (2, 0) (with γ = 1) and a spin singlet state (1, 1) (with γ = 0). To take another example, 6/13 and 6/11 map into n = 6, where we have four possible states (6, 0), (5, 1), (4,2) and (3,3), with γ = 1, 2/3, 1/3, and 0, respectively. One expects at most one transition at 2/5 and 2/3 and three at 6/13 and 6/11.…”

Section: Phase Diagram Of Spinful Cf Statesmentioning

confidence: 99%

“…It is possible to obtain very accurate numbers for many quantities of interest from the composite fermion (CF) theory [2][3][4] . Detailed comparisons have been carried out for activations gaps 5 , collective mode dispersions 6 , and spin-polarization phase transitions 3 .…”

Section: Introductionmentioning

confidence: 99%

“…Here the states remain spontaneously spin polarized even in the absence of a Zeeman energy. Spin transitions are possible for the 4 CF FQHE state at ν = n/(4n − 1), and we estimate the critical Zeeman energies for the prominent transition.…”

Section: Introductionmentioning

confidence: 99%

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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%

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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“…A composite fermion [21][22][23][24][25] is the bound state of an electron and an even number (2p) of quantized vortices. Composite fermions form Landaulike levels called Λ levels (ΛLs) in a reduced magnetic field given by B * = B − 2pρφ 0 , where ρ is the electron or CF density and φ 0 = hc/e is the flux quantum.…”

Section: Introductionmentioning

confidence: 99%

Spontaneous polarization of composite fermions in then=1Landau level of graphene

et al. 2015

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Motivated by recent experiments that reveal expansive fractional quantum Hall states in the n = 1 graphene Landau level and suggest a nontrivial role of the spin degree of freedom [Amet et al., Nat. Commun. 6, 5838 (2014)], we perform accurate quantitative study of the the competition between fractional quantum Hall states with different spin polarizations in the n = 1 graphene Landau level. We find that the fractional quantum Hall effect is well described in terms of composite fermions, but the spin physics is qualitatively different from that in the n = 0 Landau level. In particular, for the states at filling factors ν = s/(2s ± 1), s integer, a combination of exact diagonalization and the composite fermion theory shows that the ground state is fully spin polarized and supports a robust spin wave mode even in the limit of vanishing Zeeman coupling. Thus, even though composite fermions are formed, a mean field description that treats them as weakly interacting particles breaks down, and the exchange interaction between them is strong enough to cause a qualitative change in the behavior by inducing full spin polarization. We also verify that the fully spin polarized composite fermion Fermi sea has lower energy than the paired Pfaffian state at the relevant half fillings in the n = 1 graphene Landau level, indicating an absence of composite-fermion pairing at half filling in the n = 1 graphene Landau level.

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“…The most comprehensive book on quantum Hall physics is now in its 3rd edition and comprises nearly 1,000 pages (1), and new aspects of quantum Hall science are covered at the biannual international workshops entitled "Emergent Phenomena in Quantum Hall Systems" and "Electronic Properties of 2-Dimensional Systems." Many new research fields are based on quantum Hall physics, and some of them are covered by separate overviews in this journal, such as composite fermion theory of exotic fractional QHE (2), exciton condensation in bilayer quantum hall systems (3), the quantum spin hall effect (4), and quantum anomalous hall effect: theory and experiment (5). Other current topics in this field are microwave-induced resistance oscillations (6,7), and striped phases in quantum hall systems (8,9).…”

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confidence: 99%

Quantum Hall Effect: Discovery and Application

Klitzing

2017

Annu. Rev. Condens. Matter Phys.

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The unexpected discovery of the quantum Hall effect was the result of basic research on silicon field-effect transistors combined with my experience in metrology, the science of measurements. This personal review demonstrates that condensed matter physics is full of surprises and that access to excellent crystals and materials is a crucial ingredient of the success of experimentalists in condensed matter science.

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Composite Fermion Theory of Exotic Fractional Quantum Hall Effect

Cited by 38 publications

References 150 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

Spontaneous polarization of composite fermions in then=1Landau level of graphene

Quantum Hall Effect: Discovery and Application

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