Spin polarization of composite fermions and particle-hole symmetry breaking

Liu, Yang; Hasdemir, S.; Wójs, Arkadiusz; Jain, J. K.; Pfeiffer, L. N.; West, K. W.; Baldwin, K. W.; Shayegan, M.

doi:10.1103/physrevb.90.085301

Cited by 35 publications

(58 citation statements)

References 27 publications

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“…These critical Zeeman energies are in general subject to corrections due to finite thickness of the quantum well and also Landau level mixing. In GaAs both effects are present, and it is not straightforward to disentangle their contributions, although progress has been made in experiments that study the effect systematically as a function of the quantum well width 25 . Because graphene has negligible finite thickness corrections, this gives an opportunity to obtain an accurate test of the CF theory, and also to gain insight into our understanding of the role of LL mixing 17 .…”

Section: Discussionmentioning

confidence: 99%

“…Finally, there is an extensive amount of experimental phenomenology associated with the spin physics. Phase transitions as a function of the Zeeman energy have been measured in various semiconductor based two-dimensional systems [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33] , and recently also in graphene by Feldman et al…”

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: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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“…Transitions between differently spin polarized CF states can be caused by changing the Zeeman energy, and the critical Zeeman energies have been determined for many fractions for an isotropic system [74][75][76][77][78][79][80][81][82][83][84] . (These results also apply to systems with valley splitting 85,86 .)…”

Section: F Spin Phase Transitionmentioning

confidence: 99%

Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect

Balram

Jain

2016

Phys. Rev. B

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The microscopic wave functions of the composite fermion theory can incorporate electron mass anisotropy by a trivial rescaling of the coordinates. These wave functions are very likely adiabatically connected to the actual wave functions of the anisotropic fractional quantum Hall states. We show in this article that they possess the nice property that their energies can be analytically related to the previously calculated energies for the isotropic states through a universal scale factor, thus allowing an estimation of several observables in the thermodynamic limit for all fractional quantum Hall states. The rather weak dependence of the scale factor on the anisotropy provides insight into why fractional quantum Hall effect and composite fermions are quite robust to electron mass anisotropy. We discuss how better, though still approximate, wave functions can be obtained by introducing a variational parameter, following Haldane [Phys. Rev. Lett. 107, 116801 (2011)], but the resulting wave functions are not readily amenable to calculations. Our considerations are also applicable, with minimal modification, to the case where the dielectric function of the background material is anisotropic.

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“…In these experiments, the value of κ at the highest magnetic fields is κ ≈ 0.07 (assuming a g factor of 2.0 and = 3.0). In GaAs, where the spin physics of the FQHE has been investigated in detail 3,4,32 , the spin degree has been found to be relevant only for κ 0.02 32 . It is unclear why the spin degree should remain relevant up to much higher values of κ in graphene than in GaAs.…”

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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Spin polarization of composite fermions and particle-hole symmetry breaking

Cited by 35 publications

References 27 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

Exact results for model wave functions of anisotropic composite fermions in the fractional quantum Hall effect

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

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