Gauge fluctuations and interlayer coherence in bilayer composite fermion metals

Cipri, Robert; Bonesteel, N. E.

doi:10.1103/physrevb.89.085109

Cited by 16 publications

(13 citation statements)

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“…Theoretical interpretation of the intermediate phase may start from two well known limits. Starting from the infinite distance, it is nature to choose composite Fermion (CF) picture [31][32][33][34]63]. Recently, a fully gapped interlayer pairing phase is proposed based on random-phase approximation calculation [33], which is consistent with our numerical findings of flat Berry curvature as well as gapped spin-1 and charge excitations, but the explanation of finite exciton superfluid stiffness is lacking.…”

Section: E X C I T O N S U P E R F L U I Dsupporting

confidence: 73%

“…Several theoretical scenarios [22][23][24][25][26][27][28][29][30][31][32][33][34][35] have been proposed for understanding the transition between the exciton superfluid and CFL at intermediate layer distances. Due to its non-perturbative nature, controlled analytical method for this problem is still lacking, and numerical techniques have been playing an important role.…”

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confidence: 99%

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Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

Zhu

2017

Phys. Rev. Lett.

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We study the phase diagram of quantum Hall bilayer systems with total filing νT = 1/2 + 1/2 of the lowest Landau level as a function of layer distances d. Based on numerical exact diagonalization calculations, we obtain three distinct phases, including an exciton superfluid phase with spontaneous interlayer coherence at small d, a composite Fermi liquid at large d, and an intermediate phase for 1.1 < d/lB < 1.8 (lB is the magnetic length). The transition from the exciton superfluid to the intermediate phase is identified by (i) a dramatic change in the Berry curvature of the ground state under twisted boundary conditions on the two layers; (ii) an energy level crossing of the first excited state. The transition from the intermediate phase to the composite Fermi liquid is identified by the vanishing of the exciton superfluid stiffness. Furthermore, from our finite-size study, the energy cost of transferring one electron between the layers shows an even-odd effect and possibly extrapolates to a finite value in the thermodynamic limit, indicating the enhanced intralayer correlation. Our identification of an intermediate phase and its distinctive features shed new light on the theoretical understanding of the quantum Hall bilayer system at total filling νT = 1. Introduction.-The multilayer quantum Hall systems demonstrate tremendously rich physics when tuning the interlayer interaction by changing layer distance d. One of the prominent examples is the bilayer systems[1-4] at a total filling ν T = 1 (ν = 1/2 in each layer) with negligible tunneling. Experimentally, the bilayer systems can be realized in single wide quantum wells, double quantum wells or bilayer graphenes [5][6][7][8][9]. Theoretically, the quantum states in small and large d limits have been well understood. When the layer distance is small, the strong interlayer coulomb interaction drives the electron system into a pseudospin (layer) ferromagnetic long range order (FMLRO) state with the spontaneous interlayer phase coherence and interlayer superfluidity [10][11][12][13][14]. The FMLRO can also be described as an exciton condensation state as an electron in an orbit of one layer is always bound to a hole in another layer forming an exciton pair. This excitonic superfluid state can be described by Haplerin "111 state" wavefunction [15,16]. In the limit of infinite layer separation, the bilayer system reduces to two decoupled composite Fermi liquids (CFL) [17][18][19][20][21].

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Section: E X C I T O N S U P E R F L U I Dsupporting

confidence: 73%

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confidence: 99%

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

Zhu

2017

Phys. Rev. Lett.

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“…The part with (111) correlations may be followed with the Jastrow-Laughlin factors as in Eq. (25), but that will not change main conclusions reached in Ref. [30] (in the scope of a Chern-Simons (CS) description) for an intermediate phase: The pseudospin mode, which was a Goldstone mode in the (111) phase, is gapped and the phase possesses algebraic ODLRO with the exponent that depends on the ratio between densities of CBs and CFs.…”

Section: Bilayermentioning

confidence: 93%

“…The most interesting conclusion that we can draw from this application of the Dirac CF formalism is that the bosonic part necessarily acquires the additional correlations next to the basic (111), as described by Eq. (25). The ensuing presence of three gauge fields that couple to the bosonic fields may lead to fractional excitations in the low-energy sector, but not of quantized pseudospin.…”

Section: Bilayermentioning

confidence: 99%

Paired states in half-filled Landau levels

Milovanović

2017

Phys. Rev. B

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We discuss monolayer and bilayer quantum Hall systems in which each layer is a half-filled Landau level (LL) system. In the mean field approximation of the Son's formalism there is a common pairing structure that underlines the possibilities for paired ground states in both systems. We argue that the particle-hole (PH) Pfaffian state in the (particle-hole symmetric) half-filled LL of a monolayer, and analogous state in the PH symmetric bilayer (in which each layer is half-filled LL) can be considered as {\em critical states} i.e. states that cannot describe a phase under PH symmetry. We point out that the inclusion of a PH symmetry breaking (like LL mixing) may stabilize the PH Pfaffian in a monolayer. In the bilayer case, in numerical experiments on a sphere, by choosing the PH symmetric shift, we can stabilize the interlayer correlated (111) excitonic state or critical state, for any distance between the layers, but in general, with no bias, the evolution of the bilayer includes other phases.Comment: 9 pages, rewritten, published version with important conclusion

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“…We assume that the filling fraction is the same for both layers. In the imaginary time formalism, the partition function is Z ¼ R Q AE;μν is obtained with the RPA [17,18,23,24],…”

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Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers

Isobe

2017

Phys. Rev. Lett.

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We study the pairing symmetry of the interlayer paired state of composite fermions in quantum Hall bilayers. Based on the Halperin-Lee-Read (HLR) theory, the effect of the long-range Coulomb interaction and the internal Chern-Simons gauge fluctuation is analyzed with the random-phase approximation beyond the leading order contribution in small momentum expansion, and we observe that the interlayer paired states with a relative angular momentum l ¼ þ1 are energetically favored for filling ν ¼ The degeneracy between states with AEl is lifted by the interlayer density-current interaction arising from the interplay of the long-range Coulomb interaction and the Chern-Simons term in the HLR theory. DOI: 10.1103/PhysRevLett.118.166401 Quantum Hall systems with even-denominator filling fractions are well described by composite fermions (CFs) [1]. A CF in two dimensions is composed of an electron with an even number of magnetic fluxes attached via the Chern-Simons gauge field. The attached fluxes cancel the external magnetic field on average, thus leading to a welldefined Fermi surface of CFs as theorized by Halperin, Lee, and Read [2].In quantum Hall bilayer systems, quantized Hall conductances, indicative of incompressible states, are observed when each layer is at even-denominator filling fractions and two layers are separated by a short distance. Such systems are realized in a single wide quantum well [3], double quantum wells [4], and more recently, bilayer graphene [5][6][7][8]. Tunneling spectroscopy [9,10], Hall drag [11], and counterflow measurements [12,13] demonstrate the formation of an exciton superfluid phase for small layer distances [14][15][16]. On the other hand, the bilayer system is described by two composite Fermi liquids with interlayer interactions at large distance. From a theoretical viewpoint, Bonesteel et al. [17,18] showed that such a system is unstable to Cooper pairing between CFs on the two different layers. The pairing interaction arises from the long-range Coulomb interaction and fluctuations of the Chern-Simons gauge fields. Using the random-phase approximation (RPA) for the gauge field propagator, Refs. [17,18] derived the most singular part of the pairing interaction. As recognized by the authors, at this level of approximation, pairing interactions in all angular momentum channels are degenerate.In this Letter, we study the energetically favored pairing symmetry of bilayer quantum Hall systems due to the effective interaction between CFs obtained by the RPA. We go beyond the previous analyses to include the effect of the time-reversal breaking external magnetic field on the effective interaction between CFs. This effect appears through an interlayer density-current interaction mediated by the Chern-Simons gauge field. The resulting pairing interaction between CFs lifts the degeneracy between pairings in angular momentum þl and −l channels. We show that the interlayer paired state with a relative angular momentum l ¼ þ1 is favored at filling ν ¼ Model.-We consider a bilayer system o...

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Gauge fluctuations and interlayer coherence in bilayer composite fermion metals

Cited by 16 publications

References 34 publications

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

Numerical Study of Quantum Hall Bilayers at Total Filling νT=1 : A New Phase at Intermediate Layer Distances

Paired states in half-filled Landau levels

Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers

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