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

Abstract

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.

Luttinger Theorem for the Strongly Correlated Fermi Liquid of Composite Fermions

“…(Recall that, for spinful states, p-h symmetry relates ν to 2 − ν.) Extensive experimental [38][39][40][41][42][43][44][45][46][47][48][49][50] and theoretical [33,34,[51][52][53][54][55][56][57] literature on spin phase transitions has validated the explanation of the ν ¼ ðn þ 1Þ= ð2n þ 1Þ as ν Ã ¼ n þ 1 IQHE of e CFs. The validity of Ψ n=ð2nAE1Þ for the incompressible states has been established by extensive numerical studies [12,33,36,[58][59][60].…”

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

“…We predict the the critical Zeeman energy for the transition from a spin-singlet state to a fully polarized state occurs at a Zeeman energy of 0.0014(4) e 2 / . We note that in the n = 0 GLL too, for composite fermions carrying more than two vortices, 2/7 is the only filling factor in which the ground state is unpolarized 44 . As noted before, our calculation is inconclusive at ν = 3/17; due to its moderate experimental relevance we do not pursue this issue further.…”

“…As discussed previously in Ref. 44, a reliable treatment of LL mixing is a complicated task, especially because the LL mixing parameter is fairly large (greater than 1) in graphene. Nonetheless, we have estimated the corrections and found that the FQHE states remain fully spin polarized even when LL mixing is incorporated.…”

Nature of composite fermions and the role of particle-hole symmetry: A microscopic account

“…Composite fermions experience a reduced effective magnetic field and can be treated as non-interacting to a first approximation. Prominent among the successes of the composite (CF) theory are the FQHE at the Jain fractions ν = n/(2pn ± 1) (p is a positive integer), which are explained as ν * = n integer quantum Hall effect (IQHE) of composite fermions; the compressible state at ν = 1/2, which is understood as the Halperin-Lee-Read (HLR) [4] Fermi sea of composite fermions in vanishing effective magnetic field (also see Kalmeyer and Zhang [6]); the spin polarization of the FQHE states [7][8][9][10][11][12][13][14][15]; the FQHE at 5/2 [16], believed to be described by the Moore-Read Pfaffian wave function of the chiral p-wave paired state of composite fermions [17,18]; and various charged and neutral excitations that are understood as excitations of composite fermions across their Landau-like levels called Λ levels (ΛLs) [19][20][21][22][23][24][25][26][27][28][29][30][31][32][33].…”