Bilayer quantum Hall system at<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mi>ν</mml:mi><mml:mi>t</mml:mi></mml:msub><mml:mo>=</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math>: Pseudospin models and in-plane magnetic field

Tieleman, O.; Lazarides, Achilleas; Makogon, D.; Smith, C. Morais

doi:10.1103/physrevb.80.205315

Cited by 8 publications

(13 citation statements)

References 20 publications

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“…Projecting the original fermionic interacting Hamiltonian of the system into the lowest Landau level, which is completely filled ͑ =1͒, allows one to expand it in magnon states. 13 It then turns out remarkably that the dispersion relation of the free magnons coincides with the result derived by Bychkov et al 14 and also by Kallin and Halperin 15 within the fermionic description at the random-phase approximation ͑RPA͒ level and the quartic interacting part of the magnon Hamiltonian might be related to the skyrmionantiskyrmion neutral excitations of the Hall ferromagnet. 12 Moreover, in the vicinity of the ground state, without magnon-magnon interactions, magnons behave like bosons.…”

Section: Introductionsupporting

confidence: 79%

Effects of disorder and interactions in the quantum Hall ferromagnet

2010

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This work treats the effects of disorder and interactions in a quantum Hall ferromagnet, which is realized in a two-dimensional electron gas ͑2DEG͒ in a perpendicular magnetic field at Landau-level filling factor =1. We study the problem by projecting the original fermionic Hamiltonian into magnon states, which behave as bosons in the vicinity of the ferromagnetic ground state. The approach permits the reformulation of a strongly interacting model into a noninteracting one. The latter is a nonperturbative scheme that consists in treating the two-particle neutral excitations of the electron system as a bosonic single particle. Indeed, the employment of bosonization facilitates the inclusion of disorder in the study of the system. It has been shown previously that disorder may drive a quantum phase transition in the Hall ferromagnet. However, such studies have been either carried out in the framework of the nonlinear sigma model, as an effective low-energy theory, or included the long-range Coulomb interaction in a quantum description only up to the Hartree-Fock level. Here, we establish the occurrence of a disorder-driven quantum phase transition from a ferromagnetic 2DEG to a spin-glass phase by taking into account interactions between electrons up to the random-phase approximation level in a fully quantum description.

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Section: Introductionsupporting

confidence: 79%

Effects of disorder and interactions in the quantum Hall ferromagnet

2010

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“…In particular, (19)- (21) of Ref. 48, one can see that the former have extra terms. This is related to the fact that Tieleman et al approximated the bosonic representation of the operator S x (k) by linear terms, i.e., S x (k) ∼ β † k + β −k , while here the complete bosonic representation, which in addition includes a cubic term in boson operators β, is considered.…”

Section: Appendix B: Alternative Effective Boson Models For the Bilaymentioning

confidence: 88%

“…Tieleman and co-workers 48 derived an effective boson model for the bilayer QHS also following the ideas of the bosonization scheme, 13 but with some important differences: The single-particle electron states considered are no longer the pseudospin-up and -down lowest Landau levels (see Fig. 1), but symmetric and antisymmetric linear combination of these states.…”

Section: Appendix B: Alternative Effective Boson Models For the Bilaymentioning

confidence: 99%

“…Therefore, the boson operators introduced in Ref. 48, hereafter called β, differ from the bosons b discussed in Sec. II A.…”

Section: Appendix B: Alternative Effective Boson Models For the Bilaymentioning

confidence: 99%

“…Since the procedure adopted in Ref. 48 to derive an effective boson model is not fully consistent with the bosonization scheme, 13 in the following we briefly revisit its derivation.…”

Section: Appendix B: Alternative Effective Boson Models For the Bilaymentioning

confidence: 99%

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Finite-momentum condensate of magnetic excitons in a bilayer quantum Hall system

Doretto

Smith²,

Caldeira³

2012

Phys. Rev. B

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We study the bilayer quantum Hall system at total filling factor ν T = 1 within a bosonization formalism which allows us to approximately treat the magnetic exciton as a boson. We show that in the region where the distance between the two layers is comparable to the magnetic length, the ground state of the system can be seen as a finite-momentum condensate of magnetic excitons provided that the excitation spectrum is gapped. We analyze the stability of such a phase within the Bogoliubov approximation first assuming that only one momentum Q is macroscopically occupied and later we consider the same situation for two modes ±Q. We find strong evidences that a first-order quantum phase transition at small interlayer separation takes place from a zero-momentum condensate phase, which corresponds to Halperin 111 state, to a finite-momentum condensate of magnetic excitons.

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Fractional Solitons in Excitonic Josephson Junctions

Hsu

2015

Sci Rep

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The Josephson effect is especially appealing to physicists because it reveals macroscopically the quantum order and phase. In excitonic bilayers the effect is even subtler due to the counterflow of supercurrent as well as the tunneling between layers (interlayer tunneling). Here we study, in a quantum Hall bilayer, the excitonic Josephson junction: a conjunct of two exciton condensates with a relative phase ϕ0 applied. The system is mapped into a pseudospin ferromagnet then described numerically by the Landau-Lifshitz-Gilbert equation. In the presence of interlayer tunneling, we identify a family of fractional sine-Gordon solitons which resemble the static fractional Josephson vortices in the extended superconducting Josephson junctions. Each fractional soliton carries a topological charge Q that is not necessarily a half/full integer but can vary continuously. The calculated current-phase relation (CPR) shows that solitons with Q = ϕ0/2π is the lowest energy state starting from zero ϕ0 – until ϕ0 > π – then the alternative group of solitons with Q = ϕ0/2π − 1 takes place and switches the polarity of CPR.

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Bilayer quantum Hall system atνt=1: Pseudospin models and in-plane magnetic field

Cited by 8 publications

References 20 publications

Effects of disorder and interactions in the quantum Hall ferromagnet

Effects of disorder and interactions in the quantum Hall ferromagnet

Finite-momentum condensate of magnetic excitons in a bilayer quantum Hall system

Fractional Solitons in Excitonic Josephson Junctions

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