One-component to two-component transition of the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>ν</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mo>/</mml:mo><mml:mn>3</mml:mn><mml:mn /></mml:math>fractional quantum Hall effect in a wide quantum well induced by an in-plane magnetic field

Lay, T. S.; Jungwirth, T.; Smrčka, L.; Shayegan, M.

doi:10.1103/physrevb.56.r7092

Cited by 49 publications

(53 citation statements)

References 17 publications

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“…[39] the transition between a onecomponent and two-component phase was detected as a function of ∆ SAS , while in Ref. [40] similar data was obtained as a function of the tilt angle of the magnetic field. These experiments have been performed on a single wide QW.…”

Section: Experimental Backgroundmentioning

confidence: 60%

“…The gap was found to close around ∆ SAS / e 2 ǫℓB 0.1, with an incompressible phase on either side of the transition. A realistic model of this system [40], that included LDA calculation of the band structure, reproduced the observed behavior of the gap. A more complete phase diagram as a function of both d/ℓ B and ∆ SAS / e 2 ǫℓB was obtained in Ref.…”

Section: Introductionmentioning

confidence: 97%

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Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

et al. 2015

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Bilayer quantum Hall systems, realized either in two separated wells or in the lowest two sub-bands of a wide quantum well, provide an experimentally realizable way to tune between competing quantum orders at the same filling fraction. Using newly developed density matrix renormalization group techniques combined with exact diagonalization, we return to the problem of quantum Hall bilayers at filling ν = 1/3 + 1/3. We first consider the Coulomb interaction at bilayer separation d, bilayer tunneling energy ∆SAS, and individual layer width w, where we find a phase diagram which includes three competing Abelian phases: a bilayer-Laughlin phase (two nearly decoupled ν = 1/3 layers); a bilayer-spin singlet phase; and a bilayer-symmetric phase. We also study the order of the transitions between these phases. A variety of non-Abelian phases have also been proposed for these systems. While absent in the simplest phase diagram, by slightly modifying the interlayer repulsion we find a robust non-Abelian phase which we identify as the "interlayer-Pfaffian" phase. In addition to non-Abelian statistics similar to the Moore-Read state, it exhibits a novel form of bilayer-spin charge separation. Our results suggest that ν = 1/3 + 1/3 systems merit further experimental study. CONTENTS

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Section: Experimental Backgroundmentioning

confidence: 60%

Section: Introductionmentioning

confidence: 97%

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

et al. 2015

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“…Similar strengthening occurs for ν = 1/2 if the tilt is not too large. 40 Therefore, the application of the in-plane field may be a likely reason to further stabilize the (5,5,3) state at ν = 1/4 if the symmetric-antisymmetric gap ∆ SAS is sufficiently small. However, Ref.…”

Section: Discussionmentioning

confidence: 99%

Fractional quantum Hall state atν=14in a wide quantum well

Papić

Möller²,

Milovanović

et al. 2009

Phys. Rev. B

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We investigate, with the help of Monte-Carlo and exact-diagonalization calculations in the spherical geometry, several compressible and incompressible candidate wave functions for the recently observed quantum Hall state at the filling factor ν = 1/4 in a wide quantum well. The quantum well is modeled as a two-component system by retaining its two lowest subbands. We make a direct connection with the phenomenological effective-bilayer model, which is commonly used in the description of a wide quantum well, and we compare our findings with the established results at ν = 1/2 in the lowest Landau level. At ν = 1/4, the overlap calculations for the Halperin (5,5,3) and (7,7,1) states, the generalized Haldane-Rezayi state and the Moore-Read Pfaffian, suggest that the incompressible state is likely to be realized in the interplay between the Halperin (5,5,3) state and the Moore-Read Pfaffian. Our numerics shows the latter to be very susceptible to changes in the interaction coefficients, thus indicating that the observed state is of multicomponent nature.

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“…Previous observations of the ν = 1/2 state in wide GaAs quantum wells have been discussed [12] within the context of the quantity ∆ SAS , which is the energy difference between the two lowest occupied subbands in the absence of magnetic field. For a given quantum well, ∆ SAS decreases with increased density and is thought to decrease with the introduction of parallel magnetic field, B [19,20]. If we assume that ∆ SAS (estimated by calculation as ∆ SAS ≈ 30 K in our sample at B = 0) decreases with increased B then the increase in the strength of the ν = 1/2 state (Fig.…”

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confidence: 99%

Observation of a Fractional Quantum Hall State atν=1/4in a Wide GaAs Quantum Well

et al. 2008

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We report the observation of an even-denominator fractional quantum Hall (FQH) state at ν = 1/4 in a high quality, wide GaAs quantum well. The sample has a quantum well width of 50 nm and an electron density of ne = 2.55 × 10 11 cm −2 . We have performed transport measurements at T ∼ 35 mK in magnetic fields up to 45 T. When the sample is perpendicular to the applied magnetic field, the diagonal resistance displays a kink at ν = 1/4. Upon tilting the sample to an angle of θ = 20.3 o a clear FQH state at emerges at ν = 1/4 with a plateau in the Hall resistance and a strong minimum in the diagonal resistance.PACS numbers: 73.21. Fg, 73.43.Qt, 73.63.Hs Interest in the even-denominator fractional quantum Hall (FQH) state at ν = 5/2 in the first excited Landau level continues to remain high over twenty years after its discovery [1]. Generally believed to be due to the p−wave pairing of composite fermions [2,3,4,5], the quasi-particle excitations of this state are thought to obey nonabelian statistics and thus may be relevant to faulttolerant, topological quantum computing schemes [6,7].To date, observations of even-denominator FQH states have been rare beyond the ν = 5/2 state in single-layer systems [8]. In particular, experimental evidence for a FQH state at ν = 1/2, the lowest Landau level counterpart of the ν = 5/2 state, does not exist, although previous theoretical work has suggested that it may form in thick two-dimensional electrons systems (2DES) [9].In bilayer systems, however, the situation is different. The presence of two nearby interacting electron layers introduces an additional degree of freedom which can allow the formation of a FQH state at ν = 1/2. Observations of such a state at ν = 1/2 have been made in both double quantum wells [10] and wide single quantum wells (WSQWs) [11,12]. In both of these cases the ν = 1/2 state has been shown to have a large overlap with the so-called {331} wave function [13]. Originally proposed by Halperin[14] to describe two-component FQH states, the {331} wave function can also be characterized as a p−wave pairing state, although with albelian statistics [15,16,17]. A crude way to interpret the {331} wave function, or in general any {nnm} wave function, is to consider two electron layers each with a filling factor of ν * = 1/n. The electrons in each layer are bound to correlation holes in the other, represented by a filling factor of 1/m. Together the filling factor of the entire system is ν = 2/(n + m) [18].Beyond the {331} state the model should generalize to other even-denominator states. For example, both the {771} and {553} wave functions would be possible candidates to describe a FQH state at ν = 1/4. In contrast to ν = 1/2, relatively little theoretical work has been done concerning a FQH state ν = 1/4 and an experimental observation of this state has yet to be reported. On the one hand, an observation of the ν = 1/4 state would be demanding experimentally, including a high mobility 2DES and ultra high magnetic fields for high density samples. On the other ...

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One-component to two-component transition of theν=2/3fractional quantum Hall effect in a wide quantum well induced by an in-plane magnetic field

Cited by 49 publications

References 17 publications

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

Competing Abelian and non-Abelian topological orders inν=1/3+1/3quantum Hall bilayers

Fractional quantum Hall state atν=14in a wide quantum well

Observation of a Fractional Quantum Hall State atν=1/4in a Wide GaAs Quantum Well

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