Microscopic functional integral theory of quantum fluctuations in double-layer quantum Hall ferromagnets

Joglekar, Yogesh N.; MacDonald, Allan H.

doi:10.1103/physrevb.64.155315

Cited by 50 publications

(53 citation statements)

References 27 publications

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“…However, in the regime of small layer separation, an equivalent description in terms of other excitations to the 111-state may be also suitable. 5,54 It should be noted that the number of variational parameters required to obtain good trial states becomes maximal at intermediate layer separations d ∼ 1.5ℓ 0 . However, even at d ∼ 1.5ℓ 0 , only four variational parameters are required for the system sizes we consider.…”

Section: B Mixed Cf-cb Resultsmentioning

confidence: 99%

“…Conversely, for small enough spacing between the two layers the ground state is known to be the interlayer coherent "111 state", which we can think of as a composite boson (CB), or interlayer exciton condensate, 4 with strong interlayer correlations and intralayer correlations which are weaker than those of the composite fermion Fermi sea. 1 While the nature of these two limiting states is reasonably well understood, the nature of the states at intermediate d is less understood and has been an active topic of both theoretical 3,5,6,7,8,9,10,11,12,13,14,15,16 and experimental interest. 17,18,19,20,21,22,23,24,25,26,27 Although there are many interesting questions remaining that involve more complicated experimental situations, within the current work we always consider a zero temperature bilayer system with zero tunnelling between the two layers and no disorder.…”

Section: Introductionmentioning

confidence: 99%

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Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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Quantum Hall bilayer systems at filling fractions near ν = 1 2 + 1 2 undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation d is reduced below some critical value. Deep in the intralayer phase (large separation) the system can be interpreted as a fluid of composite fermions (CFs), whereas deep in the interlayer phase (small separation) the system can be interpreted as a fluid of composite bosons (CBs). The focus of this paper is to understand the states that occur for intermediate layer separation by using trial variational wavefunctions. We consider two main classes of wavefunctions. In the first class, previously introduced in Möller et al. (2003)] and generalizes the idea of pairing wavefunctions by allowing the CFs also to be replaced continuously by CBs. This generalization allows us to construct exceedingly good wavefunctions for interlayer spacings of d ℓ 0 , as well. The accuracy of the wavefunctions discussed in this work, compared with exact diagonalization, approaches that of the celebrated Laughlin wavefunction.

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Section: B Mixed Cf-cb Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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show abstract

“…For layer separations ∼ 10% below the critical value d c [52,53], quantum fluctuations in the absence of quenched disorder can be treated perturbatively [52] and will yield only small corrections to our results. In contrast, thermal fluctuations and especially in combination with disorder can modify some of our results qualitatively.…”

Section: Discussionmentioning

confidence: 99%

Critical currents of ideal quantum Hall superfluids

2003

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Filling factor ν = 1 bilayer electron systems in the quantum Hall regime have an excitoniccondensate superfluid ground state when the layer separation d is less than a critical value dc. On a quantum Hall plateau current injected and removed through one of the two layers drives a dissipationless edge current that carries parallel currents, and a dissipationless bulk supercurrent that carries opposing currents in the two layers. In this paper we discuss the theory of finite supercurrent bilayer states, both in the presence and in the absence of symmetry breaking inter-layer hybridization. Solutions to the microscopic mean-field equations exist at all condensate phase winding rates for zero and sufficiently weak hybridization strengths. We find, however, that collective instabilities occur when the supercurrent exceeds a critical value determined primarily by a competition between direct and exchange inter-layer Coulomb interactions. The critical current is estimated using a local stability criterion and varies as (dc − d) 1/2 when d approaches dc from below. For large inter-layer hybridization, we find that the critical current is limited by a soliton instability of microscopic origin.

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“…Here [9,10,11] in the region d/l ≤ 1.0. However, these previous calculations found that a minimum (roton-like excitation) appears around |ql| ∼ 1.0 for d/l > 1.0 and that this minimum becomes soft at d/l > 1.2, whereas, in our case, no minimum arises when d/l increases.…”

mentioning

confidence: 99%

Bosonization Approach for Bilayer Quantum Hall Systems atνT=1

2006

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We develop a non-perturbative bosonization approach for bilayer quantum Hall systems at νT = 1, which allows us to systematically study the existence of an exciton condensate in these systems. An effective boson model is derived and the excitation spectrum is calculated both in the Bogoliubov and in the Popov approximations. In the latter case, we show that the ground state of the system is an exciton condensate only when the distance between the layers is very small compared to the magnetic length, indicating that the system possibly undergoes another phase transition before the incompressible-compressible one. The effect of a finite electron interlayer tunnelling is included and a quantitative phase diagram is proposed.

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Microscopic functional integral theory of quantum fluctuations in double-layer quantum Hall ferromagnets

Cited by 50 publications

References 27 publications

Trial wave functions forν=12+12quantum Hall bilayers

Trial wave functions forν=12+12quantum Hall bilayers

Critical currents of ideal quantum Hall superfluids

Bosonization Approach for Bilayer Quantum Hall Systems atνT=1

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