Anomalous quantum Hall effect on sphere

Jellal, Ahmed

doi:10.1016/j.nuclphysb.2008.04.013

Cited by 17 publications

(11 citation statements)

References 48 publications

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“…This will produce reliable results for sufficiently large systems, but may have strong finite size corrections. We use an alternative approach following the direct analytical solution of the Dirac problem on a sphere by Jellal 60 . Namely, we build the spinor wave function for graphene from a pair of orbitals with the same l, and thus with different Q.…”

Section: A Exact Diagonalizationmentioning

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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Section: A Exact Diagonalizationmentioning

confidence: 99%

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

et al. 2015

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“…Therefore, we instead have adopted a direct solution of the Dirac problem on a sphere [11]. In excited LLs of graphene, the single-particle states ||n, m are spinors, whose two components represent standard LL wave functions, with equal angular momenta m but different LL indices n and n − 1.…”

Section: Interaction Pseudopotentialsmentioning

confidence: 99%

Composite Fermion Dynamics in Half-Filled Landau Levels of Graphene

2011

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We report on exact-diagonalization studies of correlated many-electron states in the half-filled Landau levels of graphene, including pseudospin (valley) degeneracy. We demonstrate that the polarized Fermi sea of non-interacting composite fermions remains stable against a pairing transition in the lowest two Landau levels. However, it undergoes spontaneous depolarization, which is unprotected owing to the lack of single-particle pseudospin splitting. These results suggest the absence of the Pfaffian phase in graphene.

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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%

“…In this work, we accomplish essentially three things: (i) One thing we do to provide an alternative derivation (compared to Jellal 28 ) of the eigenfunctions and eigenenergies for massless Dirac fermions on the Haldane sphere -our approach is more in line with the traditional approach used in the FQHE literature and utilizes the cyclotron motion operators discussed previously by Greiter 29 . Incidentally, we note that our Hamiltonian is different from that analyzed previously 25 .…”

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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Anomalous quantum Hall effect on sphere

Cited by 17 publications

References 48 publications

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

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

Composite Fermion Dynamics in Half-Filled Landau Levels 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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