Nonperturbative approach to the quantum Hall bilayer

Milovanović, M. V.; Papić, Zlatko

doi:10.1103/physrevb.79.115319

Cited by 14 publications

(28 citation statements)

References 41 publications

(67 reference statements)

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“…However, numerical studies suggest that the ground state at intermediate distance can be described by a paired state which has precisely the pairing channel considered here 27,28 . As has been previously pointed out 26 , and as we have argued employing an RG analysis, there exist a weak coupling instability to interlayer Cooper pairing in the limit of infinite layer separation.…”

Section: Summary and Discussionmentioning

confidence: 61%

“…The fate of the system is determined by the specific pairing symmetry. We will be guided by previous numerical studies of this problem showing that the composite fermions of the two layers like to form a 'pair' condensate in the p x + ip y channel as the separation d is decreased 27,28 . Interestingly, we will show the resultant paired state is smoothly connected to the exciton condensate described above.…”

Section: Bilayer Quantum Hall States Atmentioning

confidence: 99%

“…27,28 , that have been essential in motivating us to focus on the p x + ip y interlayer channel, other numerical studies had previously encountered interesting persistent aspects of exciton condensation physics to large interlayer distance, which contained important hints of the physics we have discussed. In particular, Ref.…”

Section: Halperin-lee-read Picturementioning

confidence: 99%

“…Indeed a very recent Eliashberg calculation 29 found that a p x − ip y channel is energetically favored in apparent disagreement with the numerical results in Refs. 27,28 . Additionally, other studies have advocated for alternative phases to the exciton condensate beyond some critical d [30][31][32][33][34][35] .…”

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: Summary and Discussionmentioning

confidence: 61%

Section: Bilayer Quantum Hall States Atmentioning

confidence: 99%

Section: Halperin-lee-read Picturementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Composite fermion duality for half-filled multicomponent Landau levels

et al. 2017

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“…There have been many experimental [22][23][24][25][26][27][28][29][30][31][32][33][34][35] and theoretical [36][37][38][39][40][41][42][43][44][45][46][47][48] studies regarding the nature of this transition. While some of these theoretical works point to a direct transition between the two limiting phases, either continuous 45 or of first order, 42,43 some other works predict the existence of various types of exotic intermediate phases, including translational symmetry broken phase, [36][37][38]46 composite-fermion paired state, 39,40,47 phase of coexisting composite fermions and composite bosons, 44,48,49 quantum disordered phases, 41 etc.…”

Section: Introductionmentioning

confidence: 99%

Clausius-Clapeyron relations for first-order phase transitions in bilayer quantum Hall systems

et al. 2010

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A bilayer system of two-dimensional electron gases in a perpendicular magnetic field exhibits rich phenomena. At total filling factor tot = 1, as one increases the layer separation, the bilayer system goes from an interlayer-coherent exciton condensed state to an incoherent phase of, most likely, two decoupled compositefermion Fermi liquids. Many questions still remain as to the nature of the transition between these two phases. Recent experiments have demonstrated that spin plays an important role in this transition. Assuming that there is a direct first-order transition between the spin-polarized interlayer-coherent quantum Hall state and spin partially polarized composite Fermi-liquid state, we calculate the phase boundary ͑d / l͒ c as a function of parallel magnetic field, NMR/heat pulse, temperature, and density imbalance, and compare with experimental results. Remarkably good agreement is found between theory and various experiments.

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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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Nonperturbative approach to the quantum Hall bilayer

Cited by 14 publications

References 41 publications

Composite fermion duality for half-filled multicomponent Landau levels

Composite fermion duality for half-filled multicomponent Landau levels

Clausius-Clapeyron relations for first-order phase transitions in bilayer quantum Hall systems

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

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