Stripe Formation in the Fractional Quantum Hall Regime

Lee, Seung Yeop; Scarola, V. W.; Jain, J. K.

doi:10.1103/physrevlett.87.256803

Cited by 76 publications

(125 citation statements)

References 33 publications

(34 reference statements)

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“…In Fig. 1(d) we plot V QE (R) obtained more recently by Lee et al 22 using a somewhat different approach. Since it confirms the oscillatory behavior at short range in Fig.…”

Section: Qp Interactionsmentioning

confidence: 97%

“…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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“…In Fig. 1(d) we plot V QE (R) obtained more recently by Lee et al 22 using a somewhat different approach. Since it confirms the oscillatory behavior at short range in Fig.…”

Section: Qp Interactionsmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Fractional quantum Hall states of clustered composite fermions

2004

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“…In general, the values of the CF pseudopotentials are obtained with an uncertainty of .01% or less. 18,19 We refer the reader to the literature for further details. 14,18,19,28,29 We next define a problem of fermions confined to the lowest LL that have an effective interaction V eff (r) that produces the above pseudopotentials:…”

Section: A Two-body Interaction Between Composite Fermionsmentioning

confidence: 99%

“…[15][16][17]. The type-II CFWC was also studied by Scarola et al 18,19 and by Goerbig et al 20 in a variational study that compared the energies of the WC, bubble crystal, or stripe phases of composite fermions; these works, however, did not compute the shear modulus of the CFWC or the magnetophonon and magnetoplasmon dispersions. Our main conclusions are as follows.…”

Section: Introductionmentioning

confidence: 99%

Static and dynamic properties of type-II composite fermion Wigner crystals

Archer

Jain

2011

Phys. Rev. B

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The Wigner crystal of composite fermions is a strongly correlated state of complex emergent particles in two dimensions, and therefore its unambiguous detection would be of significant importance. Recent observation of optical resonances in the vicinity of filling factor ν = 1/3 has been interpreted as evidence for a pinned Wigner crystal of composite fermions [Zhu et al., Phys. Rev. Lett. 105, 126803 (2010)]. We evaluate in a microscopic theory the shear modulus and the magnetophonon and magnetoplasmon dispersions of the composite fermion Wigner crystal in the vicinity of filling factors 1/3, 2/5, and 3/7. We determine the region of stability of the crystal phase, and also relate the frequency of its pinning mode to that of the corresponding electron crystal near integer fillings. These results are in good semiquantitative agreement with experiment, and therefore support the identification of the optical resonance as the pinning mode of the composite fermions Wigner crystal. Our calculations also bring out certain puzzling features, such as a relatively small melting temperature for the composite fermion Wigner crystal, and also suggest a higher asymmetry between Wigner crystals of composite fermion particles and holes than that observed experimentally.

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“…Such typical concepts include the generalized master equations and their corresponding statistical quantifiers [29][30][31][32][33]], Lee's recurrence relation method [34][35][36][37], the generalized Langevin equation [38][39][40][41], the tailored generalized master equation approach for studying the ageing effects in systems with non-Poisson distribution [42], to name only a few. Likewise, the kinetic approaches of Zwanzig and Mori [43][44][45][46][47] are one of the most simple analytical methods for studying the statistical memory effects in various systems such as the ones being considered here.…”

Section: Theoretical Description Of Memory Effects In Discrete Stochamentioning

confidence: 99%

Statistical quantifiers of memory for an analysis of human brain and neuro-system diseases

Demin

Yulmetyev

Panischev

et al. 2008

Physica A: Statistical Mechanics and its Applications

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On the basis of a memory function formalism for correlation functions of time series we investigate statistical memory effects by the use of appropriate spectral and relaxation parameters of measured stochastic data for neuro-system diseases. In particular, we study the dynamics of the walk of a patient who suffers from Parkinson's disease (PD), Huntington's disease (HD), amyotrophic lateral sclerosis (ALS), and compare against the data of healthy people (CO -control group). We employ an analytical method which is able to characterize the stochastic properties of stride-to-stride variations of gait cycle timing. Our results allow us to estimate quantitatively a few human locomotion function abnormalities occurring in the human brain and in the central nervous system (CNS). Particularly, the patient's gait dynamics are characterized by an increased memory behavior together with sizable fluctuations as compared with the locomotion dynamics of healthy patients. Moreover, we complement our findings with peculiar features as detected in phase-space portraits and spectral characteristics for the different data sets (PD, HD, ALS and healthy people). The evaluation of statistical quantifiers of the memory function is shown to provide a useful toolkit which can be put to work to identify various abnormalities of locomotion dynamics. Moreover, it allows one to diagnose qualitatively and quantitatively serious brain and central nervous system diseases.

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Stripe Formation in the Fractional Quantum Hall Regime

Cited by 76 publications

References 33 publications

Fractional quantum Hall states of clustered composite fermions

Fractional quantum Hall states of clustered composite fermions

Static and dynamic properties of type-II composite fermion Wigner crystals

Statistical quantifiers of memory for an analysis of human brain and neuro-system diseases

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