State counting for excited bands of the fractional quantum Hall effect: Exclusion rules for bound excitons

Balram, Ajit C.; Wójs, Arkadiusz; Jain, J. K.

doi:10.1103/physrevb.88.205312

Cited by 47 publications

(60 citation statements)

References 40 publications

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“…Detailed comparisons have been carried out for activations gaps 5 , collective mode dispersions 6 , and spin-polarization phase transitions 3 . In all cases, the measured numbers are generally consistent with those predicted by theory, but the agreement is worse than that suggested by the accuracy of the theory as determined from comparisons with exact diagonalization results 3,[7][8][9] . It is believed that the deviation arises from corrections due to effects extraneous to the FQHE physics, such as finite quantum well width, Landau level (LL) mixing and disorder, which are substantial and hard to deal with in a quantitative manner.…”

Section: Introductionsupporting

confidence: 68%

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: Introductionsupporting

confidence: 68%

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

et al. 2015

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“…The trial wave functions given by the CF theory are not very accurate quantitatively for the 7/3 ground state and excitations (see, e.g., Ref. 43), but are the best available model that can be dealt with in a simple manner. We find that, within this model, the edge of the 7/3 state is also reconstructed for d 0.5 B .…”

Section: Introductionmentioning

confidence: 99%

Theoretical investigation of edge reconstruction in theν=52and73fractional quantum Hall states

Zhang

Hutasoit

et al. 2014

Phys. Rev. B

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The edge physics of the ν = 5/2 fractional quantum Hall state is of relevance to several recent experiments that use it as a probe to gain insight into the nature of the bulk state. We perform calculations in a semi-realistic setup with positive background charge at a distance d, by exact diagonalization both in the full Hilbert space (neglecting Landau level mixing) and in the restricted Pfaffian basis of edge excitations. Our principal finding is that the 5/2 edge is unstable to a reconstruction except for very small d. In addition, the interactions between the electrons in the second Landau level and the lowest Landau level enhance the tendency toward edge reconstruction. We identify the bosonic and fermionic modes of edge excitations and obtain their dispersions by back-calculating from the energy spectra as well as directly from appropriate trial wave functions. We find that the edge reconstruction is driven by an instability in the fermionic sector for setback distances close to the critical ones. We also study the edge of the ν = 7/3 state and find that edge reconstruction occurs here more readily than for the ν = 1/3 state. Our study indicates that the ν = 5/2 and 7/3 edge states are reconstructed for all experimental systems investigated so far and thus must be taken into account when analyzing experimental results. We also consider an effective field theory to gain insight into how edge reconstruction might influence various observable quantities.

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“…Furthermore, their low-energy excitations are obtained by exciting composite fermions across ΛLs 24,36,70 . Our motivation for investigating the excitations comes from the fact that spin reversed excitations of composite fermions can reveal an instability of the fully polarized ground state at sufficiently small Zeeman energies.…”

Section: Excitationsmentioning

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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State counting for excited bands of the fractional quantum Hall effect: Exclusion rules for bound excitons

Cited by 47 publications

References 40 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

Theoretical investigation of edge reconstruction in theν=52and73fractional quantum Hall states

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

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