Quasiparticle interactions in fractional quantum Hall systems: Justification of different hierarchy schemes

Wójs, Arkadiusz; Quinn, John J.

doi:10.1103/physrevb.61.2846

Cited by 77 publications

(137 citation statements)

References 65 publications

(74 reference statements)

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“…Being equivalent to the CF hierarchy 10 of Laughlincorrelated spin-polarized QP states, not only are these models not conceptually new, but they are also unjustified at the QP fillings in question. 8 In fact, some of the numerical results obtained earlier in a slightly different context 11,12 and more detailed results presented here show that they do not describe the new FQH states.…”

Section: Introductionmentioning

confidence: 87%

“…The qualitative behavior of V QP (R) at short range is well-known from the numerical studies of small systems. 8,21,22,23 In Fig. 1(b) we compare V QE (R) calculated for the systems of N = 8 to 12 electrons.…”

Section: Qp Interactionsmentioning

confidence: 99%

“…1 that the pseudopotential for the interacting CF-QH's is similar to that of QE's. To confirm this, we have calculated this pseudopotential in a standard way, 8 by numerical diagonalization of N QH's interacting through V QH in a shell of angular momentum…”

Section: Corresponding Qe and Qh Statesmentioning

confidence: 99%

“…8,11,30,31 However, it must be carefully noticed that the predicted absence of Laughlin correlations does not preclude the FQH effect itself, only a microscopic origin of the effect attributable to Laughlin correlations. It should also be realized that immediate application of the CF model without studying the interactions between the relevant particles (electrons, QP's, etc.)…”

Section: Pseudopotentials Laughlin Correlations and The Composimentioning

confidence: 99%

“…Standard numerical calculations for N e electrons are not useful for studying the new states, because convincing results require too large values of N e . Therefore, we take advantage of the knowledge 8,21,22,23 of the dominant features of the pseudopotential V QE (R) of the QE-QE interaction (i.e., the QE-QE interaction energy V QE as a function of relative pair angular momentum R), and diagonalize the (much smaller) interaction Hamiltonian of the N -QE systems. This procedure was earlier shown 21 to accurately reproduce the low-energy N e -electron spectra at filling factors ν between 1 3 and 2 5 .…”

Section: Introductionmentioning

confidence: 99%

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Fractional quantum Hall states of clustered composite fermions

2004

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The energy spectra and wavefunctions of up to 14 interacting quasielectrons (QE's) in the Laughlin ν = 1 3 fractional quantum Hall (FQH) state are investigated using exact numerical diagonalization. It is shown that at sufficiently high density the QE's form pairs or larger clusters. This behavior, opposite to Laughlin correlations, invalidates the (sometimes invoked) reapplication of the composite fermion picture to the individual QE's. The series of finite-size incompressible ground states are identified at the QE filling factors νQE = 1 2 , 1 3 , 2 3 , corresponding to the electron fillings ν = 3 8 , 4 11 , 5 13 . The equivalent quasihole (QH) states occur at νQH = 1 4 , 1 5 , 2 7 , corresponding to ν = 3 10 , 4 13 , 5 17 . All these six novel FQH states were recently discovered experimentally. Detailed analysis indicates that QE or QH correlations in these states are different from those of well-known FQH electron states (e.g., Laughlin or Moore-Read states), leaving the origin of their incompressibility uncertain. Halperin's idea of Laughlin states of QP pairs is also explored, but is does not seem adequate.

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Section: Introductionmentioning

confidence: 87%

Section: Qp Interactionsmentioning

confidence: 99%

Section: Corresponding Qe and Qh Statesmentioning

confidence: 99%

Section: Pseudopotentials Laughlin Correlations and The Composimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fractional quantum Hall states of clustered composite fermions

2004

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Photoluminescence of the Incompressible Laughlin Liquid: Excitons, Charged Excitons, and Fractionally Charged Excitons

Wójs

2001

phys. stat. sol. (b)

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The photoluminescence (PL) of a two-dimensional electron gas (2DEG) in a high magnetic field is studied as a function of the filling factor and the separation d between the electron layer and the valence hole. Depending on the magnitude of d relative to the magnetic length l, two distinct regimes in the response of the 2DEG to the valence hole occur, with different elementary emission processes contributing to the PL spectrum. At d < l (''strong coupling" regime), the hole binds one or two electrons to form an exciton (X) or one of three possible charged exciton (X À ) states, a spinsinglet or one of two spin-triplets. At d > l (''weak coupling" regime), the hole decouples or binds one or two Laughlin quasi-electrons to form fractionally charged excitons (FCXs). The binding energies as well as the emission energies and intensities of all X À and FCX states are calculated.

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