Fermionic Chern-Simons theory of SU(4) fractional quantum Hall effect

Modak, S; Mandal, Sudhansu S.; Sengupta, K.

doi:10.1103/physrevb.84.165118

Cited by 14 publications

(43 citation statements)

References 29 publications

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“…In the SU(4) generalization [13] of CF theory [19,20], the orbital part of the ground state wave function at ν = m/(2pm ± 1) for correlated electrons in the maximal weight states [25] of an SU(4) multiplet at monopole strength Q is still given by equation 2, but with , it is easy to see that Ψ satisfies Fock's cyclic condition [25], i.e., it is annihilated by any attempt to antisymmetrize an electron l of type u (min u ≤ l ≤ max u ) with respect to the electrons of type t < u,…”

Section: Su(4) Analysismentioning

confidence: 99%

Multi-component fractional quantum Hall states in graphene:SU(4) versusSU(2)

Tőke¹,

Jain²

2012

J. Phys.: Condens. Matter

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Abstract. Because of the spin and Dirac-valley degrees of freedom, graphene allows the observation of one-, two-or four-component fractional quantum Hall effect in different parameter regions. We address the stability of various states in the SU(2) and SU(4) limits. In the SU(4) limit, we predict that new low-energy Goldstone modes determine the stability of the fractional quantum Hall states at 2/5, 3/7 etc.; SU(4) skyrmions are not found to be relevant for the low-energy physics. These results are discussed in light of experiments.

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Section: Su(4) Analysismentioning

confidence: 99%

Multi-component fractional quantum Hall states in graphene:SU(4) versusSU(2)

Tőke¹,

Jain²

2012

J. Phys.: Condens. Matter

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“…When disorder is low and at high magnetic field, Coulomb forces between electrons become important and many-body effects emerge. Recently, the fractional quantum Hall effect (FQHE) of Dirac fermions has attracted considerable attention [10][11][12][13][14][15][16][17][18][19][20][21][22][23] . In graphene, the low dielectric constant and unique band structure lead to fractional quantum Hall states with energy gaps that are larger than in GaAs at the same field, particularly in the N = 1 LL 11,17,18 .Moreover, the SU(4) symmetry of charge carriers in graphene could yield fractional quantum Hall states without analogues in GaAs 12-14 .…”

mentioning

confidence: 99%

Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene

Feldman

Krauß

Smet

et al. 2012

Science

185

274

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Application of a strong perpendicular magnetic field B to a two-dimensional electron gas effectively quenches the kinetic energy of electrons and gives rise to flat energy bands called Landau levels (LLs) which contain a total of eB/h states, where e is the electron charge and h is Planck's constant. In graphene, each of these states has an additional fourfold degeneracy due to the spin and sublattice degrees of freedom, and the LLs possess an approximate SU(4) LLs. This occurs in graphene at filling factors Ȟ = neB/h = 4(N + 1/2) in the absence of interelectron interactions 7-9 , where n is the charge carrier density and N is the orbital index.Hence, the quantum Hall sequence is shifted by a half-integer, a distinctive signature that reflects the sublattice pseudospin of graphene.When disorder is low and at high magnetic field, Coulomb forces between electrons become important and many-body effects emerge. Recently, the fractional quantum Hall effect (FQHE) of Dirac fermions has attracted considerable attention [10][11][12][13][14][15][16][17][18][19][20][21][22][23] . In graphene, the low dielectric constant and unique band structure lead to fractional quantum Hall states with energy gaps that are larger than in GaAs at the same field, particularly in the N = 1 LL 11, 17, 18 .Moreover, the SU(4) symmetry of charge carriers in graphene could yield fractional quantumHall states without analogues in GaAs 12-14 . The FQHE was recently observed [24][25][26] in suspended graphene samples at Ȟ = 1/3 and 2/3, with an activation gap at Ȟ = 1/3 of approximately 2 meV at B = 14 T. Measurements of graphene on hexagonal boron nitride substrates 27 revealed further fractional quantum Hall states at all multiples of Ȟ = 1/3 up to 13/3, except at Ȟ = 5/3, but no conductance plateaus were observed at filling factors with higher denominators. It was suggested that the absence of a fractional quantum Hall state at Ȟ = 5/3 might result from lowlying excitations associated with SU(2) or SU(4) symmetry, but alternate scenarios associated with disorder could not be ruled out 27 .Here we report local electronic compressibility measurements of graphene performed using a scanning single-electron transistor (SET) 28, 29 . We observe a unique pattern of incompressible fractional quantum Hall states at filling factors with odd denominators as large as nine. Figure 1a shows a schematic of the measurement setup. By modulating the carrier density 4 and monitoring the resulting change in SET current, we measure both the local chemical potential µ and the local inverse electronic compressibility dµ/dn of the graphene flake.The inverse electronic compressibility as a function of carrier density and magnetic field is shown in Fig. 1b. At zero magnetic field, we observe an incompressible peak that arises from the vanishing density of states at the charge neutrality point in graphene. For B > 0, strong incompressible behavior occurs at Ȟ = 4(N + 1/2), confirming the monolayer nature of our sample. In addition to the expected single-particle quan...

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“…We have studied Chern-Simon's wave function (k 1 , k 2 , n) for the SU(2) case, which is described by the exponent matrix [21]…”

Section: Composite Fermion-chern Simon's Theorymentioning

confidence: 99%

Study of partially polarized fractional quantum Hall states

2018

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We have studied the partially spin polarized fractional quantum Hall states using Chern Simon's theory and plasma picture proposed by Halperin. Using these theoretical techniques we have tried to find the stable polarized states of different filling fractions observed in experiments. We have calculated the ground state energies of those states and also pair correlation function. We have described the nature of the states by the behavior of this quantity. In our study, we have seen that the partially polarized states, which do not fit with Jain's composite fermion description are basically the mixed state of up-spin liquid phase and down-spin solid phase.

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Fermionic Chern-Simons theory of SU(4) fractional quantum Hall effect

Cited by 14 publications

References 29 publications

Multi-component fractional quantum Hall states in graphene:SU(4) versusSU(2)

Multi-component fractional quantum Hall states in graphene:SU(4) versusSU(2)

Unconventional Sequence of Fractional Quantum Hall States in Suspended Graphene

Study of partially polarized fractional quantum Hall states

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