Composite Fermion Dynamics in Half-Filled Landau Levels of Graphene

Wójs, Arkadiusz; Möller, Gunnar; Cooper, N. R.

doi:10.12693/aphyspola.119.592

Cited by 11 publications

(15 citation statements)

References 12 publications

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“…But the similarity ends here as the recently published results [23,24] indicate the absence of a non--Abelian Pfaan phase in graphene.…”

Section: Discussionsupporting

confidence: 90%

Quasi-Particle Localization by Disorder in ν = 5/2 Fractional Quantum Hall State and Its Potential Application

Goswami

2012

Acta Phys. Pol. A

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We consider the lling factor 5/2 fractional quantum Hall state of spin-polarized fermions in a dirty (mobility µ b < 10 m 2 V −1 s −1 ) bi-layer quantum well system.We show that the system undergoes a quantum phase transition from the eective two-component state to an eective single-component state, at xed charge imbalance regulatory parameter ∆c and constant layer separation, as the inter-layer tunneling strength ∆SAS is increased. At nite and constant ∆SAS, a transition from the latter state to the former state is also possible upon increasing the parameter ∆c. We identify the order parameter to describe quantum phase transition as a pseudo-spin component and calculate this with the aid of the Matsubara propagators in the nite-temperature formalism. Our treatment is able to show that, at low temperature(< 0.1 K) and low value of charge imbalance regulatory parameter, there is a competition between the disorder and the inter-layer tunneling strength in the sample. The competition leads to the quasi-particle localization at low tunneling strength.

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“…But the similarity ends here as the recently published results [23,24] indicate the absence of a non--Abelian Pfaan phase in graphene.…”

Section: Discussionsupporting

confidence: 90%

Quasi-Particle Localization by Disorder in ν = 5/2 Fractional Quantum Hall State and Its Potential Application

Goswami

2012

Acta Phys. Pol. A

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“…Furthermore, the fully spin polarized CFFS has the lowest energy. Even though the CF wave function for the spin singlet CFFS is not as accurate as that for the fully polarized CFFS, the energy difference between them is sufficiently large that we are confident in concluding that the ground state at ν = 1/2 in the n = 0 GLL is the fully spin polarized CFFS even at zero Zeeman energy 42,43 . For contrast, we also show results for two different interactions.…”

Section: Excitationsmentioning

confidence: 80%

“…Namely, we build the spinor wave function for graphene from a pair of orbitals with the same l, and thus with different Q. This leads to the expression for a spinor matrix element in graphene through the scalar matrix elements in GaAs, all derived in spherical geometry and hence all behaving properly at any range 42,59 :…”

Section: A Exact Diagonalizationmentioning

confidence: 99%

“…Given that filling factor ν = 1/2 in the n = 1 LL of GaAs produces an incompressible state, it is natural to ask if the same is true in graphene. This question has been addressed in the past using both exact diagonalization 42 and methods of CF theory 41 , and it was concluded that the Pfaffian states is not favored. For completeness, we have addressed this issue with our more accurate real-space interaction.…”

Section: Excitationsmentioning

confidence: 99%

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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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“…Refs. 23-25 and 26 and 27) the recent work 20,22 was justified by appealing to a calculation of the eigenstates by Jellal 28 .…”

Section: Introductionmentioning

confidence: 99%

Landau level quantization for massless Dirac fermions in the spherical geometry: Graphene fractional quantum Hall effect on the Haldane sphere

Arciniaga

Peterson

2016

Phys. Rev. B

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We derive the single-particle eigenenergies and eigenfunctions for massless Dirac fermions confined to the surface of a sphere in the presence of a magnetic monopole, i.e., we solve the Landau level problem for electrons in graphene on the Haldane sphere. With the single-particle eigenfunctions and eigenenergies we calculate the Haldane pseudopotentials for the Coulomb interaction in the second Landau level and calculate the effective pseudopotentials characterizing an effective Landau level mixing Hamiltonian entirely in the spherical geometry to be used in theoretical studies of the fractional quantum Hall effect in graphene. Our treatment is analogous to the formalism in the planar geometry and reduces to the planar results in the thermodynamic limit.

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Composite Fermion Dynamics in Half-Filled Landau Levels of Graphene

Cited by 11 publications

References 12 publications

Quasi-Particle Localization by Disorder in ν = 5/2 Fractional Quantum Hall State and Its Potential Application

Quasi-Particle Localization by Disorder in ν = 5/2 Fractional Quantum Hall State and Its Potential Application

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

Landau level quantization for massless Dirac fermions in the spherical geometry: Graphene fractional quantum Hall effect on the Haldane sphere

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