Phase Diagram 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>5</mml:mn><mml:mo stretchy="false">/</mml:mo><mml:mn>2</mml:mn></mml:math>Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width

Peterson, Michael R.; Pakrouski, Kiryl; Jolicœur, Thierry; Scarola, V. W.; Nayak, Chetan; Troyer, Matthias

doi:10.1103/physrevx.5.021004

Cited by 94 publications

(76 citation statements)

References 88 publications

(185 reference statements)

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“…According to some of recent theories [22,23,27], the anti-Pfaffian state might be preferred to the MR Pfaffian state. On the contrary, another recent theory argues that the MR Pfaffian might be favored in some range of the Landau level mixing parameter [28].…”

Section: Introductionmentioning

confidence: 91%

Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing

Jeong

Park

2015

Phys. Rev. B

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One of the most dominant candidates for the paired quantum Hall (QH) state at filling factor ν = 5/2 is the Moore-Read (MR) Pfaffian state. A salient problem, however, is that it does not occur exactly at the Coulomb interaction, but rather at a modified interaction, which favors particle-hole symmetry breaking. In an effort to find a better state, in this work, we investigate the possible connection between the paired QH state and the antisymmetrized bilayer ground state, which is inspired by the intriguing identity that the MR Pfaffian state is entirely equivalent to the antisymmetrized projection of the bilayer QH state called the Halperin (331) state, which is valid at interlayer distance, d, roughly equal to the magnetic length, lB. Specifically, by using exact diagonalization in the torus geometry, we show that the exact 5/2 state at a given Haldane pseudopotential variation is intimately connected with the antisymmetrized bilayer ground state at a corresponding d/lB via one-to-one mapping, which we call the bilayer mapping. One of the most important discoveries in this work is that the paired QH state occurring at the Coulomb interaction is mapped onto the antisymmetrized bilayer ground state at d ≫ lB, which is equivalent to the antisymmetrized product state of two composite fermion seas at quarter filling, not the MR Pfaffian state. While maintaining high overlap with the paired QH state, the antisymmetrized bilayer ground state at d ≫ lB exhibits an abrupt change under the influence of small anisotropy. This suggests that the paired QH state occurring at the Coulomb interaction might be susceptible to anisotropic instability, opening up the possibility of anisotropic px or py-wave pairing instead of px ± ipy-wave pairing in the MR Pfaffian/anti-Pfaffian state.

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Section: Introductionmentioning

confidence: 91%

Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing

Jeong

Park

2015

Phys. Rev. B

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“…Later in this work we add additional V α terms to V C in order to explore the neighboring phases. In experiment, such variations of the interaction may arise due to Landau level mixing [48,[87][88][89][90][91][92][93][94].…”

Section: A the Bilayer Modelmentioning

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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“…In the Moore-Read Pfaffian state 24,25 and the anti-Pfaffian state, 40,41 proposed as candidate non-Abelian states for the 5/2-FQHS, charge-e/4 quasiparticles are Ising anyons. 26,[42][43][44][45][46][47][48] There is theoretical 28,[49][50][51][52][53][54][55][56] and experimental [29][30][31][32][57][58][59][60][61][62] evidence that the ν = 5/2 fractional quantum Hall state is in one of these two universality classes. However, there are also some experiments [63][64][65][66] that do not agree with this hypothesis.…”

Section: Mzms In Topological Phases and In Topological Superconductorsmentioning

confidence: 99%

Majorana zero modes and topological quantum computation

2015

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We provide a current perspective on the rapidly developing field of Majorana zero modes (MZMs) in solid-state systems. We emphasise the theoretical prediction, experimental realisation and potential use of MZMs in future information processing devices through braiding-based topological quantum computation (TQC). Well-separated MZMs should manifest non-Abelian braiding statistics suitable for unitary gate operations for TQC. Recent experimental work, following earlier theoretical predictions, has shown specific signatures consistent with the existence of Majorana modes localised at the ends of semiconductor nanowires in the presence of superconducting proximity effect. We discuss the experimental findings and their theoretical analyses, and provide a perspective on the extent to which the observations indicate the existence of anyonic MZMs in solid-state systems. We also discuss fractional quantum Hall systems (the 5/2 state), which have been extensively studied in the context of non-Abelian anyons and TQC. We describe proposed schemes for carrying out braiding with MZMs as well as the necessary steps for implementing TQC. INTRODUCTIONTopological quantum computation 1,2 is an approach to faulttolerant quantum computation in which the unitary quantum gates result from the braiding of certain topological quantum objects called 'anyons'. Anyons braid non-trivially: two counterclockwise exchanges do not leave the state of the system invariant, unlike in the cases of bosons or fermions. Anyons can arise in two ways: as localised excitations of an interacting quantum Hamiltonian 3 or as defects in an ordered system.

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Phase Diagram of theν=5/2Fractional Quantum Hall Effect: Effects of Landau-Level Mixing and Nonzero Width

Cited by 94 publications

References 88 publications

Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing

Bilayer mapping of the paired quantum Hall state: Instability toward anisotropic pairing

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

Majorana zero modes and topological quantum computation

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