Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene

Lin, Xi; Du, Rui-Rui; Xie, X. C.

doi:10.1093/nsr/nwu071

Cited by 50 publications

(44 citation statements)

References 240 publications

(293 reference statements)

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“…The observation of FQHE in graphene [10][11][12][13][14][15][16] provides a unique opportunity in this context, because finite width corrections are essentially absent in graphene. Furthermore, as noted by Peterson and Nayak 17 , unlike in GaAs quantum wells, in the n = 0 LL of graphene, LL mixing does not produce any effective three body interaction (which incorporates the breaking of particle-hole symmetry), but only corrections to the pairwise interaction.…”

Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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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.

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Section: Introductionmentioning

confidence: 99%

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

et al. 2015

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“…In order to systematically study the correlation physics in the N=1 LL, recent work has also been focused on the reentrant integer quantum Hall effect (RIQHE) around ν=5/2 [16][17][18][19][20][21]. In the N=2 LL, RIQHE between ν=4 and ν=5 integer quantum Hall effect (IQHE) has been observed in the square samples, with filling factors generally believed to be ~4.25 and ~4.75 [17,22,23].…”

Section: Introductionmentioning

confidence: 99%

Depinning transition of bubble phases in a high Landau level

Wang

et al. 2015

Phys. Rev. B

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In the higher Landau levels (N>0) a reentrant integer quantum Hall effect (RIQHE) state, which resides at fractional filling factors but exhibiting integer Hall plateaus, has been previously observed and studied extensively. The nonlinear dynamics of RIQHE were measured by microwave resonance, with the results consistent with an electronic bubble phase pinned by impurities. We have carried out Introduction In condensed matter systems nonlinear dynamics are commonly associated with a class of translational-symmetry-broken phases, often termed electronic crystals. Archetypical examples include Wigner crystals (WC), striped phase in high T c superconductors, charge order in organic materials, and charged colloidal crystals. Among these, nonlinear transport of the charge density wave (CDW) has been studied extensively [1,2], where CDW is pinned by impurities in a small bias regime. Its dynamics can be revealed by dramatic transport behaviors, such as threshold electric field (E T ) and conductance steps resulting from the de-pinning transition in an increasing bias. In the quantum Hall system which is realized in a two-dimensional electron gas (2DEG) under an intensive magnetic field, the WC, striped, and bubble phases have been observed [3][4][5][6][7][8][9][10][11][12][13]. In order to understand the nonlinear dynamics of these phases, it is of great interest to directly measure their critical transport parameters, such as thresholds for the de-pinning. However, such information is often obscured by off-diagonal component of the conductance tensor under magnetic fields.

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“…These Dirac materials have revived experimental and theoretical research of quasi-relativistic particles in systems of different dimensions 14,15 . 2-dimensional systems are especially of interest due to graphene, 2D topological insulators and the fractional quantum Hall effect 16 . Research is focused on bound states of Dirac particles for example in the context of quantum computing and waveguides 17,18 .…”

Section: Introductionmentioning

confidence: 99%

Confining massless Dirac particles in two-dimensional curved space

et al. 2018

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Dirac particles have been notoriously difficult to confine. Implementing a curved space Dirac equation solver based on the quantum Lattice Boltzmann method, we show that curvature in a 2-D space can confine a portion of a charged, mass-less Dirac fermion wave-packet. This is equivalent to a finite probability of confining the Dirac fermion within a curved space region. We propose a general power law expression for the probability of confinement with respect to average spatial curvature for the studied geometry.

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Recent experimental progress of fractional quantum Hall effect: 5/2 filling state and graphene

Cited by 50 publications

References 240 publications

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

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

Depinning transition of bubble phases in a high Landau level

Confining massless Dirac particles in two-dimensional curved space

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