-Wave Pairing in Quantum Hall Bilayers

Papić, Zlatko; Milovanović, M. V.

doi:10.1155/2011/614173

Cited by 6 publications

(8 citation statements)

References 21 publications

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“…We also note that other numerical studies have advocated the possibility of the disappearance of the exciton condensate at interlayer distances beyond a critical value [31][32][33][34] . In particular, one simple yet non-trivial test that any particle-hole symmetric state must satisfy is that the shift in the sphere must be S = 1…”

Section: Halperin-lee-read Picturementioning

confidence: 57%

“…Reference 27 argued that this shift persists to intermediate distances. Other studies 33,34 have countered this by arguing for the possibility of a phase transition at which the shift changes. We hope that our work motivates further numerical studies that attempt to settle the nature of the ground state at intermediate interlayer distances.…”

Section: Halperin-lee-read Picturementioning

confidence: 99%

“…27,28 . Additionally, other studies have advocated for alternative phases to the exciton condensate beyond some critical d [30][31][32][33][34][35] . We will not attempt to wade into this issue here.…”

Section: Introductionmentioning

confidence: 99%

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Composite fermion duality for half-filled multicomponent Landau levels

et al. 2017

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We study the interplay of particle-hole symmetry and fermion-vortex duality in multicomponent half-filled Landau levels, such as quantum Hall gallium arsenide bilayers and graphene. For the ν=1/2+1/2 bilayer, we show that particle-hole-symmetric interlayer Cooper pairing of composite fermions leads to precisely the same phase as the electron exciton condensate realized in experiments. This equivalence is easily understood by applying the recent Dirac fermion formulation of ν=1/2 to two components. It can also be described by Halperin-Lee-Read composite fermions undergoing interlayer px+ipy pairing. An RG analysis showing strong instability to interlayer pairing at large separation d → ∞ demonstrates that two initially-decoupled composite Fermi liquids can be smoothly tuned into the conventional bilayer exciton condensate without encountering a phase transition. We also discuss multicomponent systems relevant to graphene, derive related phases including a Z2 gauge theory with spin-half visons, and argue for symmetry-enforced gaplessness under full SU(N f ) flavor symmetry when the number of components N f is even.

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Section: Halperin-lee-read Picturementioning

confidence: 57%

Section: Halperin-lee-read Picturementioning

confidence: 99%

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Composite fermion duality for half-filled multicomponent Landau levels

et al. 2017

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“…This wavefunction encodes the physics of exciton superfluidity, with an associated Goldstone mode [77] and vanishing of Hall resistivity in the "counterflow" measurement setup [78,79]. The existence of an incompressible state (consistent with an exciton superfluid) has been established in numerics [80][81][82][83][84] The case of total filling ν = 2/3, which is the subject of this paper, has been less studied compared to previous examples. In the mentioned Ref.…”

Section: Experimental Backgroundmentioning

confidence: 97%

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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“…Currently, there are three typical lines of work that use: composite bosons (CB) [11,12], composite fermions (CF) [13][14][15][16][17][18][19], and both composite bosons and fermions [20][21][22]. Moreover, the importance of these theories is enhanced because not only explain the quantum Hall effect but they are also related to superconductivity [23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic Interaction of Composite Particles in a Higher-Derivative Nonrelativistic Gauge Field Model

Manavella

Repetto

2012

Int J Theor Phys

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A higher-derivative classical nonrelativistic U(1) × U(1) gauge field model that describes the electromagnetic interaction of composite particles in 2 + 1 dimensions is proposed. The model contains a Chern-Simons U(1) field and the electromagnetic U(1) field, and it uses either a composite boson system or a composite fermion one. The second case is explicitly considered. The model is obtained by adding suitable higher-derivative terms to the Lagrangian of a model previously proposed. One of them for the electromagnetic field and the other for the Chern-Simons field. By following the usual Hamiltonian method for singular higher-derivative systems, the canonical quantization is carried out. By extending the Faddeev-Senjanovic formalism, the path integral quantization is developed. Consequently, the Feynman rules are established and the diagrammatic structure is discussed. In this context, only a mixed bosonic propagator can be defined. The use of the higherderivative terms eliminates the ultraviolet divergence of the primitively divergent Feynman diagrams where the bosonic propagator is present. The unitarity problem, related to the possible appearance of states with negative norm, is treated. A generalization of the BecchiRouet-Stora-Tyutin algorithm is applied to the model. We will focus our attention on the issue from the point of view of the field theory.

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-Wave Pairing in Quantum Hall Bilayers

Cited by 6 publications

References 21 publications

Composite fermion duality for half-filled multicomponent Landau levels

Composite fermion duality for half-filled multicomponent Landau levels

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

Electromagnetic Interaction of Composite Particles in a Higher-Derivative Nonrelativistic Gauge Field Model

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