Activation gaps of fractional quantum Hall effect in the second Landau level

Choi, Hee Cheul; Kang, W.; Sarma, S. Das; Pfeiffer, L. N.; West, K. W.

doi:10.1103/physrevb.77.081301

Cited by 119 publications

(133 citation statements)

References 28 publications

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“…The simplest one is varying the chemical potential to place the system in a higher Landau level, effectively at filling ν = 8/3, where FQHE has been seen [119][120][121]. More recent sample fabrication techniques also allow to access the regime of large Landau level mixing (with the mixing parameter κ 2 [122,123]), which is expected to strongly modify the short-range components of the Coulomb interaction.…”

Section: Discussionmentioning

confidence: 99%

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: Discussionmentioning

confidence: 99%

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

et al. 2015

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“…The existence of a neighboring single layer non-Abelian state in the phase diagram, which can be realized by tuning the interlayer tunneling/repulsion, suggests that experiments have a chance of realizing this transition. Furthermore, recent detailed experimental studies of the energy gaps of the ν = 8/3 FQH state in single-layer systems indicate that it might be an exotic state, as opposed to a conventional Laughlin or hierarchy state [15]. This observation, together with the result of this paper that the Z 4 parafermion state lies close to the experimentally observed (330) state in the quantum Hall phase diagram, suggests that the Z 4 parafermion state ought to be considered as a candidate -in addition to other proposed possibilities (e.g.…”

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confidence: 99%

Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States

Barkeshli

Wen

2010

Phys. Rev. Lett.

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We find a series of possible continuous quantum phase transitions between fractional quantum Hall (FQH) states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p, p, p − 3) Abelian two-component state while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν = 2/3 and single-component systems at ν = 8/3.One of the most challenging problems in the study of quantum many-body systems is to understand transitions between topologically ordered states [1]. Since topological states cannot be characterized by broken symmetry and local order parameters, we cannot use the conventional Ginzburg-Landau theory. When nonAbelian topological states are involved, the transitions that are currently understood are essentially all equivalent to the transition between weak and strong-paired BCS states [2,3]. Over the last ten years, while there has been much work on the subject, there has not been another quantum phase transition in a physically realizable system, involving a non-Abelian phase, for which we can answer the most basic questions of whether the transition can be continuous and what the critical theory is. Here we present an additional example in the context of fractional quantum Hall (FQH) systems.The quasiparticle excitations in FQH states carry fractional statistics and fractional charge [1]. In particular, in a (ppq) bilayer FQH state [1,4], there is a type of excitation, called a fractional exciton (f-exciton), which is a bound state of a quasiparticle in one layer and an oppositely charged quasihole in the other layer. It carries fractional statistics. As we increase the repulsion between the electrons in the two layers, the energy gap of the f-exciton will be reduced; when it is reduced to zero, the f-exciton will condense and drive a phase transition. When the anyon number has only a mod n conservation, this can even lead to a non-Abelian FQH state [2], yet little is known about "anyon condensation" [5][6][7][8]. A better understanding of these phase transitions may aid the quest for experimental detection of non-Abelian FQH states, because one side of the transition -in our case the (330) state at ν = 2/3 -can be accessed experimentally [9,10]. The results of this paper suggest a new way of experimentally tuning to a non-Abelian state in bilayer FQH states, similar to the transition from the (331) state to the Moore-Read Pfaffian at ν = 1/2 [2, 3, 11].In the (ppq) state, when the energy gap of the f-exciton at k = 0 is reduced to zero, the f-exciton will condense [2]. The transition can be described by the φ = 0 → φ = 0 transition in a Ginzburg-Landau theory with a Chern-where θ is the statistical angle of the f-exciton. Suc...

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“…Including the nite thickness eect (FTE) it was shown [25,18] that in the LLL (n = 0) (and the SLL (n = 1))…”

Section: Introductionmentioning

confidence: 99%

“…We consider two nite thickness potential models [25,18], viz. (i) the innite square-well (SQ) potential which is appropriate for 2D GaAs quantum well structures, and (ii) the FangHoward (FH) variational potential for a heterostructure.…”

Section: Introductionmentioning

confidence: 99%

Quasi-Particle Localization by Disorder in ν = 5/2 Fractional Quantum Hall State and Its Potential Application

Goswami

2012

Acta Phys. Pol. A

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We consider the lling factor 5/2 fractional quantum Hall state of spin-polarized fermions in a dirty (mobility µ b < 10 m 2 V −1 s −1 ) bi-layer quantum well system.We show that the system undergoes a quantum phase transition from the eective two-component state to an eective single-component state, at xed charge imbalance regulatory parameter ∆c and constant layer separation, as the inter-layer tunneling strength ∆SAS is increased. At nite and constant ∆SAS, a transition from the latter state to the former state is also possible upon increasing the parameter ∆c. We identify the order parameter to describe quantum phase transition as a pseudo-spin component and calculate this with the aid of the Matsubara propagators in the nite-temperature formalism. Our treatment is able to show that, at low temperature(< 0.1 K) and low value of charge imbalance regulatory parameter, there is a competition between the disorder and the inter-layer tunneling strength in the sample. The competition leads to the quasi-particle localization at low tunneling strength.

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Activation gaps of fractional quantum Hall effect in the second Landau level

Cited by 119 publications

References 28 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

Anyon Condensation and Continuous Topological Phase Transitions in Non-Abelian Fractional Quantum Hall States

Quasi-Particle Localization by Disorder in ν = 5/2 Fractional Quantum Hall State and Its Potential Application

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