Composite fermions and Landau-level mixing in the fractional quantum Hall effect

Melik-Alaverdian, V.; Bonesteel, N. E.

doi:10.1103/physrevb.52.r17032

Cited by 47 publications

(49 citation statements)

References 12 publications

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“…But, we find that both effects, taken together, produce a further reduction. Our results are in direct contrast to what has been found in the lowest Landau levels [79,80] where both effects were not found to be additive.…”

Section: Energy Gapscontrasting

confidence: 99%

Phase Diagram of theν=5/2Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width

et al. 2015

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Interesting non-Abelian states, e.g., the Moore-Read Pfaffian and the anti-Pfaffian, offer candidate descriptions of the ν ¼ 5=2 fractional quantum Hall state. But, the significant controversy surrounding the nature of the ν ¼ 5=2 state has been hampered by the fact that the competition between these and other states is affected by small parameter changes. To study the phase diagram of the ν ¼ 5=2 state, we numerically diagonalize a comprehensive effective Hamiltonian describing the fractional quantum Hall effect of electrons under realistic conditions in GaAs semiconductors. The effective Hamiltonian takes Landau-level mixing into account to lowest order perturbatively in κ, the ratio of the Coulomb energy scale to the cyclotron gap. We also incorporate the nonzero width w of the quantum-well and subband mixing. We find the ground state in both the torus and spherical geometries as a function of κ and w. To sort out the nontrivial competition between candidate ground states, we analyze the following four criteria: its overlap with trial wave functions, the magnitude of energy gaps, the sign of the expectation value of an order parameter for particle-hole symmetry breaking, and the entanglement spectrum. We conclude that the ground state is in the universality class of the Moore-Read Pfaffian state, rather than the anti-Pfaffian, for κ < κ c ðwÞ, where κ c ðwÞ is a w-dependent critical value 0.6 ≲ κ c ðwÞ ≲ 1. We observe that both Landau-level mixing and nonzero width suppress the excitation gap, but Landau-level mixing has a larger effect in this regard. Our findings have important implications for the identification of non-Abelian fractional quantum Hall states.

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Section: Energy Gapscontrasting

confidence: 99%

Phase Diagram of theν=5/2Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width

et al. 2015

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“…). Qualitatively, it is seen that the FQH states are very robust to LL-mixing, at least as far as the transport gaps are concerned (which has been pointed out before [6,8,9]). While the calculations which leave out the electronic HF energy in H n ′ n ′ show a linear dependence on κ, the ones which include the HF energy show a much more physical behavior, with results that are even more robust under LL-mixing.…”

Section: Resultsmentioning

confidence: 90%

“…However, as the field is lowered, the question of LL-mixing becomes unavoidable, and must be accounted for theoretically. Previous approaches to this issue have been based on exact diagonalizations [6] or the Quantum Monte Carlo method [7][8][9] on finite systems.…”

Section: Discussionmentioning

confidence: 99%

“…However, when one wishes to make detailed comparisons between the theory and experiment, say in the study of transport gaps, one must seek corrections due to the nonzero value of κ, that is, include the effects of Landau level mixing. Hitherto these effects have been studied numerically [6][7][8], with the latest results coming from a fixed-phase diffusion Monte Carlo study [9].…”

Section: Introductionmentioning

confidence: 99%

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Hamiltonian theory of the fractional quantum Hall effect: Effect of Landau level mixing

Murthy

Shankar

2002

Phys. Rev. B

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We derive an effective hamiltonian in the Lowest Landau Level (LLL) that incorporates the effects of Landau-level mixing to all higher Landau levels to leading order in the ratio of interaction energy to the cyclotron energy, κ = (e 2 /εl)/ωc. We then transcribe the hamiltonian to the composite fermion basis using our hamiltonian approach and compute the effect of LL mixing on transport gaps. 73.50.Jt,

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“…Finally, it is known that the short-range Coulomb interactions are softened in 2DES with large  [33,34]. Consequently, FQHE becomes less stable.…”

mentioning

confidence: 99%

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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Composite fermions and Landau-level mixing in the fractional quantum Hall effect

Cited by 47 publications

References 12 publications

Phase Diagram of theν=5/2Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width

Phase Diagram of theν=5/2Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width

Hamiltonian theory of the fractional quantum Hall effect: Effect of Landau level mixing

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

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