Rotons of composite fermions: Comparison between theory and experiment

Scarola, V. W.; Park, Kwon; Jain, J. K.

doi:10.1103/physrevb.61.13064

Cited by 82 publications

(114 citation statements)

References 37 publications

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“…Despite some inconsistencies with the NICF, the agreement between the ED and energies obtained from the CF trial wave functions 13,27 suggests that the lowest excitations are well-defined modes whose wave vector k is proportional to the spatial quasiparticle-quasihole separation. Rough estimates of the k → ϱ energies are summarized in Table I.…”

Section: Polarized States-summarymentioning

confidence: 99%

“…2͑a͒. The dispersion structure with two minima was found a long time ago ͑on a torus, 26 sphere, 38 and using projected 27 or unprojected 20 trial wave functions of CF magnetorotons͒ and the goal of Fig. 2 is to summarize all ED data accessible with present-day computers.…”

Section: Excitations From the Polarized Ground Statesmentioning

confidence: 99%

“…1͑a͒, consists of a particle promoted to the ͑2,↑͒ CF Landau level interacting with a hole in the ͑1,↑͒ level and this interpretation agrees with the CF trial-wave-function calculation. 27 Starting with intuitive electrostatics, the interaction energy as a function of the mutual distance between a quasiparticle and a quasihole will be minimised if their overlap is maximal. Wave functions of a particle or hole in the second and first Landau level have two extrema ͑one extremum͒ and it is likely that combining two such objects may lead to more than just one local minimum in E͑kᐉ 0 ͒.…”

Section: Excitations From the Polarized Statesmentioning

confidence: 99%

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Charge-spin excitations of the Ising-type fractional quantum Hall ferromagnets

et al. 2009

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We study the low-lying excitations from the fractional quantum Hall states at filling factors 2/3 and 2/5 and argue that the charge-carrying excitations involve spin flips, and, in particular, possibly more than one. Energies obtained by exact diagonalization and transport activation gaps measured over a wide range of magnetic fields are invoked. We discuss the relevance of the noninteracting composite-fermion picture where both fractions correspond to the same filling factor 2 of the composite fermions. DOI: 10.1103/PhysRevB.80.045407 PACS number͑s͒: 73.43.Ϫf, 75.10.Lp, 73.63.Ϫb In Jain's composite-fermion ͑CF͒ picture, 1 incompressible electron states 2 of the fractional quantum Hall ͑FQH͒ effect 3 form pairs corresponding to the same magnitude of the effective magnetic field B ‫ء‬ acting on the CFs. For example, the distinct FQH states at Landau-level ͑LL͒ filling factors =2/ 5 and 2/3 both correspond to two effective LLs completely filled with the CFs, i.e., to the same effective filling factor ‫ء‬ = 2. These states are distinguished by the orientation of B ‫ء‬ with respect to the real magnetic field acting on the electrons. Some properties of these FQH systems are known and can be understood using the mentioned analogy, for instance the Ising-like transition between ground states ͑GS͒ of different magnetization ͑paramagnetic and ferromagnetic͒, 4,5 some other properties are known but the applicability of the composite-fermion picture is not established, like the existence of a half-polarized ground state 6 ͑whose microscopic origin is still debated͒, 7 and some are not explored yet. It was found in a previous study that the measured gaps for =2/ 5 and 2/3 showed different dependences on magnetic field which was interpreted using different g factors for CFs. 8 However, no detailed calculations were undertaken at that time to understand this observed effect. Exactdiagonalization ͑ED͒ studies could clarify the underlying physics. Can charged excitations exist at these filling factors that carry large spin? If so, how far can these excitations be understood using the CF picture? Such excitations, identified as skyrmions, 9 do exist at filling factor 1 and its CF counterpart =1/ 3 which are Heisenberg-like quantum Hall ferromagnets ͑QHF͒, 10 as shown by numerous experimental and theoretical arguments. 11 They may be viewed as an extension of the idea of FQH quasiparticles involving single spin flip. 12 Systems at filling factors 2/5 and 2/3 define a wider field for research, first because of their two possible GS ͑polarized and spin singlet͒, second because there are no analytical models for large spin quasiparticles such as skyrmions, and also because the similarity between 2/5 and 2/3 on the CF level can be tested. In this paper, we investigate the lowest excited states of these ‫ء‬ = 2 systems and present arguments for the spin flips being involved.We begin by a recapitulation of known properties for = 2 in Sec. I. The following section first deals with how this knowledge is transferred to the fractional ...

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Section: Polarized States-summarymentioning

confidence: 99%

Section: Excitations From the Polarized Ground Statesmentioning

confidence: 99%

Section: Excitations From the Polarized Statesmentioning

confidence: 99%

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Charge-spin excitations of the Ising-type fractional quantum Hall ferromagnets

et al. 2009

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“…E * Z is the large wavevector limit (q → ∞) of the spin wave mode. (b) The thick line is the dispersion of the CM excitation (after Scarola et al [23]). The dotted line is a schematic representation for the spin wave dispersion.…”

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confidence: 99%

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

Dujovne¹,

Hirjibehedin²,

Pinczuk³

et al. 2003

Solid State Communications

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Resonant inelastic light scattering experiments access the low lying excitations of electron liquids in the fractional quantum Hall regime in the range 2/5 ≥ ν ≥ 1/3. Modes associated with changes in the charge and spin degrees of freedom are measured. Spectra of spin reversed excitations at filling factor ν 1/3 and at ν 2/5 identify a structure of lowest spin-split Landau levels of composite fermions that is similar to that of electrons. Observations of spin wave excitations enable determinations of energies required to reverse spin. The spin reversal energies obtained from the spectra illustrate the significant residual interactions of composite fermions. At ν = 1/3 energies of spin reversal modes are larger but relatively close to spin conserving excitations that are linked to activated transport. Predictions of composite fermion theory are in good quantitative agreement with experimental results. The fractional quantum Hall effect (FQHE) is an electron condensation phenomenon that occurs at low temperatures when two-dimensional electron systems of very low disorder are exposed to high magnetic fields. The FQH states are archetypes of quantum fluids that emerge in low dimensional electron systems due to the impact of fundamental interactions. In the FQHE the 2D electron system becomes incompressible at certain values of the Landau level filling factor ν = nhc/eB, where n is the electron density and B is the perpendicular magnetic field. In the filling factor range 1 ≥ ν ≥ 1/3 the major sequence of the FQHE occurs at 'magic' filling factors ν = p/(2p ± 1), where p is an integer. The composite fermion (CF) framework interprets the sequence by attaching two vortices of the many body wavefunction to each electron [1,2]. Chern-Simons gauge fields incorporate electron interactions so that CF's experience effective magnetic fields B * = B − B 1/2 = ±B/(2p ± 1), where B 1/2 is the perpendicular magnetic field at ν = 1/2 [3, 4, 5]. Composite fermion quasiparticles have spin-split energy levels characteristic of charged fermions with spin 1/2 moving in the effective magnetic field B * . The levels resemble spin-split Landau levels of electrons. The number p thus becomes the CF Landau level filling factor and in FQHE states at ν = p/(2p ± 1) there are p fully occupied levels of composite fermions.Structures of spin-split CF levels are shown schematically in Fig. 1 for ν 1/3 and ν 2/5. The spacing between sequential CF levels with same spin is represented as a cyclotron frequency [3,6,7,8,9,10,11,12], ω c = eB * /cm CF , where m CF is a CF effective mass. Figure 1 also presents the transitions of composite fermions near filling factors 1/3 and 2/5. The charge mode (CM) transitions are spin-conserving. The spin wave (SW) and spin flip (SF) transitions involve a spin-reversal. The CM transition energies, however, could be different from CF level spacings. The difference is due to the changes in self-interaction energies that may occur when quasiparticles and quasiholes are created [9].Neutral pair excitations of quasiparti...

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“…This effect is understood as the manifestation of a collective state -the incompressible quantum Hall liquid [3,4]. The electrons in this state do not behave like independent particles, but respond to external perturbations as a single entity: in particular, they exhibit collective density oscillations (collective modes) similar to phonons in a solid, with the crucial difference that in the long-wavelength limit, the frequency tends to a finite value (the q 0 gap) [5][6][7]. Light scattering experiments [8][9][10] have confirmed the existence of a gapped collective mode, whose frequency decreases with decreasing wavelength.…”

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confidence: 99%

New Collective Mode in the Fractional Quantum Hall Liquid

Tokatly

Vignale²

2007

Phys. Rev. Lett.

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We apply the methods of continuum mechanics to the study of the collective modes of the fractional quantum Hall liquid. Our main result is that at long-wavelength, there are two distinct modes of oscillations, while previous theories predicted only one. The two modes are shown to arise from the internal dynamics of shear stresses created by the Coulomb interaction in the liquid. Our prediction is supported by recent light scattering experiments, which report the observation of two long-wavelength modes in a quantum Hall liquid. DOI: 10.1103/PhysRevLett.98.026805 PACS numbers: 73.21.ÿb, 73.43.ÿf, 78.35.+c, 78.30.ÿj The two-dimensional electron liquid in semiconductor heterostructures is a remarkable many-body system. At low temperature and high magnetic field, it exhibits the fractional quantum Hall effect [1,2] whereby the Hall resistance assumes a universal value, independent of material parameters. This effect is understood as the manifestation of a collective state -the incompressible quantum Hall liquid [3,4]. The electrons in this state do not behave like independent particles, but respond to external perturbations as a single entity: in particular, they exhibit collective density oscillations (collective modes) similar to phonons in a solid, with the crucial difference that in the long-wavelength limit, the frequency tends to a finite value (the q 0 gap) [5][6][7]. Light scattering experiments [8][9][10] have confirmed the existence of a gapped collective mode, whose frequency decreases with decreasing wavelength. However, they have also revealed the existence of a second mode [11] at filling factor 1=3-the most prominent of the quantum Hall fractions-whose frequency increases with decreasing wavelength. What is the origin of the second mode? In the past, there have been suggestions that two long-wavelength modes might arise from some interaction between free and bound pairs of short wavelength excitations, known as rotons [12,13]. Here we provide a sharper answer, based on a recently developed continuum mechanics approach [14] to the dynamics of incompressible liquids. The existence of two collective modes is shown to be a direct consequence of the dynamics of the shear stresses created by the Coulomb interaction in the incompressible liquid. In both modes, a small element of the liquid performs a circular motion, driven by the combined action of the ordinary shear force and the Lorentz shear force (the nature of these forces will be elucidated below). The sense of rotation is opposite for the two modes. In the standard mode, the two shear forces act in the same direction, while in the new mode, they act in opposite directions. Our approach enables us to calculate the dispersion and the splitting of the two modes in terms of elastic moduli, which are determined from sum rules and self-consistency conditions. The calculated dispersions are in qualitative agreement with the experiment at 1=3 [11]. Furthermore, we predict the splitting of the modes to be a common feature of fractional quantum Hall liquid...

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Rotons of composite fermions: Comparison between theory and experiment

Cited by 82 publications

References 37 publications

Charge-spin excitations of the Ising-type fractional quantum Hall ferromagnets

Charge-spin excitations of the Ising-type fractional quantum Hall ferromagnets

Light scattering observations of spin reversal excitations in the fractional quantum Hall regime

New Collective Mode in the Fractional Quantum Hall Liquid

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