Gauge Fields and Pairing in Double-Layer Composite Fermion Metals

Bonesteel, N. E.; McDonald, Ian A.; Nayak, Chetan

doi:10.1103/physrevlett.77.3009

Cited by 124 publications

(159 citation statements)

References 19 publications

(19 reference statements)

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“…1 For large enough spacing, the two layers interact very weakly and must be essentially independent ν = 1 2 states, which can be described as compressible composite fermion (CF) Fermi seas. 2 So long as the distance between the two layers is very large, there are very strong intralayer correlations but very weak interlayer correlations (although, as we will discuss below, even very weak interlayer correlations may create a pairing instability at exponentially low temperatures 3 ). Conversely, for small enough spacing between the two layers the ground state is known to be the interlayer coherent "111 state", which we can think of as a composite boson (CB), or interlayer exciton condensate, 4 with strong interlayer correlations and intralayer correlations which are weaker than those of the composite fermion Fermi sea.…”

Section: Introductionmentioning

confidence: 99%

“…Conversely, for small enough spacing between the two layers the ground state is known to be the interlayer coherent "111 state", which we can think of as a composite boson (CB), or interlayer exciton condensate, 4 with strong interlayer correlations and intralayer correlations which are weaker than those of the composite fermion Fermi sea. 1 While the nature of these two limiting states is reasonably well understood, the nature of the states at intermediate d is less understood and has been an active topic of both theoretical 3,5,6,7,8,9,10,11,12,13,14,15,16 and experimental interest. 17,18,19,20,21,22,23,24,25,26,27 Although there are many interesting questions remaining that involve more complicated experimental situations, within the current work we always consider a zero temperature bilayer system with zero tunnelling between the two layers and no disorder.…”

Section: Introductionmentioning

confidence: 99%

“…Some very influential works have pointed to the possibility that a number of exotic phases could be lurking within this transition as well. 3,9,10,11,14,31 In particular, it has been suggested 3,11,12 that the bilayer CF Fermi sea is always unstable to BCS pairing from weak interactions between the two layers (due to gauge field fluctuations). Some of these works 11,12 further concluded that the pairing of CFs should be in the p x − ip y channel, which would be analogous to the pairing that occurs in single layer CF systems to form the Moore-Read Pfaffian state 32,33 from the CF Fermi sea.…”

Section: Introductionmentioning

confidence: 99%

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Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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Quantum Hall bilayer systems at filling fractions near ν = 1 2 + 1 2 undergo a transition from a compressible phase with strong intralayer correlation to an incompressible phase with strong interlayer correlations as the layer separation d is reduced below some critical value. Deep in the intralayer phase (large separation) the system can be interpreted as a fluid of composite fermions (CFs), whereas deep in the interlayer phase (small separation) the system can be interpreted as a fluid of composite bosons (CBs). The focus of this paper is to understand the states that occur for intermediate layer separation by using trial variational wavefunctions. We consider two main classes of wavefunctions. In the first class, previously introduced in Möller et al. (2003)] and generalizes the idea of pairing wavefunctions by allowing the CFs also to be replaced continuously by CBs. This generalization allows us to construct exceedingly good wavefunctions for interlayer spacings of d ℓ 0 , as well. The accuracy of the wavefunctions discussed in this work, compared with exact diagonalization, approaches that of the celebrated Laughlin wavefunction.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Trial wave functions forν=12+12quantum Hall bilayers

Möller¹,

Simon²,

Rezayi

2009

Phys. Rev. B

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“…[16][17][18][19][20][21] Although we understand well both the coherent phase at d / l → 0 and the composite Fermi-liquid state at d / l → ϱ, the transition between them has been shrouded in mystery. 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,…”

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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“…Finally, we do not have a good understanding of the nature of the quantum phase transition or transitions that occur as the layer spacing is increased. Various scenarios have been suggested theoretically 26,16,18 and there is some numerical evidence hinting that there is a single weakly first order transition. 11…”

mentioning

confidence: 99%

Broken Symmetry and Josephson-Like Tunnelling in Quantum Hall Bilayers

Girvin

2002

Recent Progress in Many-Body Theories

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I review recent novel experimental and theoretical advances in the physics of quantum Hall effect bilayers. Of particular interest is a broken symmetry state which optimizes correlations by putting the electrons into a coherent superposition of the two different layers.The various quantum Hall effects are among the most remarkable many-body phenomena discovered in the second half of the twentieth century. 1, 2, 3, 4 The fractional effect has yielded fractional charge, spin and statistics, as well as unprecedented order parameters. 5 There are beautiful connections with a variety of different topological and conformal field theories of interest in nuclear and high energy physics.The quantum Hall effect (QHE) takes place in a two-dimensional electron gas formed in a quantum well in a semiconductor host material and subjected to a very high magnetic field. In essence it is a result of a commensuration between the number of electrons, N , and the number of flux quanta, N Φ , in the applied magnetic field. The electrons condense into distinct and highly non-trivial ground states ('vacua') formed at each rational fractional value of the filling factor ν ≡ N/N Φ .The essential feature of (most) of these exotic states is the existence of an excitation gap. The electron fluid is incompressible and flows rigidly past obstacles (impurities in the sample) with no dissipation. A weak external electric field will cause the fluid to move, but the excitation gap prevents the fluid from absorbing any energy from the electric field. Hence the current flow must be exactly at right angles to the field and the conductivity tensor takes the remarkable universal formIronically, this ideal behavior occurs because of imperfections and disorder in the samples which localize topological defects (vortices) whose motion would otherwise dissipate energy. In a two-dimensional superconductor, such vortices undergo a confinement phase transition at the Kosterlitz-Thouless temperature and dissipation ceases. In most cases in the QHE, an analog of the Anderson-Higgs mechanism causes the vortices to be deconfined 5 so that dissipation is strictly zero only at zero temperature. In practice, values of σ xx /σ xy as small as 10 −13 are not difficult to obtain at dilution refrigerator tempertures. Recent technological progress in molecular beam epitaxy techniques has led to the ability to produce pairs of closely spaced two-dimensional electron gases. Strong correlations between the electrons in different layers lead a great deal of completely new physics involving spontaneous interlayer phase coherence. 6,

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Gauge Fields and Pairing in Double-Layer Composite Fermion Metals

Abstract: Typeset using REVT E X 1

Cited by 124 publications

References 19 publications

Trial wave functions forν=12+12quantum Hall bilayers

Trial wave functions forν=12+12quantum Hall bilayers

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

Broken Symmetry and Josephson-Like Tunnelling in Quantum Hall Bilayers

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