Spin in fractional quantum Hall systems

Výborný, Karel

doi:10.1002/andp.200610228

Cited by 6 publications

(18 citation statements)

References 67 publications

(190 reference statements)

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“…Now, let us turn our attention to = 1 as an analogy of the =1/ 3 system and also the =2/ 3 polarized system by virtue of the particle-hole symmetry. 22 The ͑identical͒ excitation spectra of the =1/ 3 and 2/3 fully polarized systems contain the magnetoroton mode which gives the lowest excitation at nonzero k as expected for a ͑1,↑͒ particle interacting with a ͑0,↓͒ hole. The real charge densities of quasiparticles and quasiholes at =1/ 3 and 2/5 ͑see Appendix D͒ qualitatively support the validity of this interpretation.…”

Section: Excitations From the Polarized Statesmentioning

confidence: 83%

“…An important difference to the integral quantum Hall effect is, however, that the CF Landau levels are "generated" by the electron-electron interaction. Following the standard procedure, 22 all numerically calculated energies reported in this paper are obtained by diagonalizing the "ideal system" many-body Hamiltonian…”

Section: Theoretical Expectations For Fractional Fillingsmentioning

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: Excitations From the Polarized Statesmentioning

confidence: 83%

Section: Theoretical Expectations For Fractional Fillingsmentioning

confidence: 99%

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

et al. 2009

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“…The filling factor is ν = N/N m when N electrons are put into the rectangle. The Haldane pseudopotentials can be defined in this geometry, too, albeit they no longer correspond to eigenstates of angular momentum 37 .…”

Section: A Exact Diagonalizationmentioning

confidence: 99%

“…Experimental techniques to achieve this situation (tilted magnetic field, g-factor reduced by hydrostatic pressure etc.) are summarized elsewhere 37,44 .…”

Section: B Quantum Hall Ferromagnetsmentioning

confidence: 99%

Integral and fractional quantum Hall Ising ferromagnets

et al. 2007

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We compare quantum Hall systems at filling factors ν = 2 to ν = 2 3 and 2 5 , corresponding to the exact filling of two lowest electron or composite fermion (CF) Landau levels. The two fractional states are examples of CF liquids with spin dynamics. There is a close analogy between the ferromagnetic (spin polarization P = 1) and paramagnetic (P = 0) incompressible ground states that occur in all three systems in the limits of large and small Zeeman spin splitting. However, the excitation spectra are different. At ν = 2, we find spin domains at half-polarization (P = 1 2 ), while antiferromagnetic order seems most favorable in the CF systems. The transition between P = 0 and 1, as seen when e.g. the magnetic field is tilted, is also studied by exact diagonalization in toroidal and spherical geometries. The essential role of an effective CF-CF interaction is discussed, and the experimentally observed incompresible half-polarized state is found in some models.

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“…To evaluate this integral, we write the elliptic θ functions in Ψ nj as infinite sums, see also [55,59]. We get…”

Section: Discussionmentioning

confidence: 99%

Fractional quantum Hall states of a Bose gas with a spin–orbit coupling

Graß¹,

Juliá-Dı́az²,

Burrello³

et al. 2013

J. Phys. B: At. Mol. Opt. Phys.

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We study the fractional quantum Hall phases of a pseudospin-1/2 Bose gas in an artificial gauge field. In addition to an external magnetic field, the gauge field also mimics an intrinsic spin-orbit coupling of the Rashba type. While the spin degeneracy of the Landau levels is lifted by the spin-orbit coupling, the crossing of two Landau levels at certain coupling strengths gives rise to a new degeneracy. We therefore take into account two Landau levels, and perform exact diagonalization of the many-body Hamiltonian. We study and characterize the quantum Hall phases which occur in the vicinity of the degeneracy point. Notably, we describe the different states appearing at the Laughlin fillings, ν = 1/2 and ν = 1/4. While for these filling factors incompressible phases disappear at the degeneracy point, denser systems at ν = 3/2 and ν = 2 are found to be clearly gapped. For filling factors ν = 2/3 and ν = 4/3, we discuss the connection of the exact ground state to the non-Abelian spin singlet states, obtained as the ground state of k + 1 body contact interactions.

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Spin in fractional quantum Hall systems

Cited by 6 publications

References 67 publications

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

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

Integral and fractional quantum Hall Ising ferromagnets

Fractional quantum Hall states of a Bose gas with a spin–orbit coupling

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