Trial wave functions forν=12+12quantum Hall bilayers

Abstract

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.

Fractional quantum Hall state atν=14in a wide quantum well

“…There have been generalizations of these wave functions in the physics of bilayer systems at total filling factor 24,25,26 ν = 1 and to more than two components, 27 where further constraints on the possible values of m, m ′ , n were derived within the plasma analogy. 28 In a two-component case, these turn out to be the intuitive requirement that "intra"-component interactions are stronger than "inter"-component interactions: m, m ′ ≥ n. For the particular case of two components and m = m ′ = n + 2 (which includes Ψ 331 and Ψ 553 ), the Halperin wave function (5) can be analytically cast into a paired form 26,29 via Cauchy determinant identity (up to the unimportant phase factor),…”

Interlayer Pairing Symmetry of Composite Fermions in Quantum Hall Bilayers

“…[20] without energetics. On the other hand, numerical studies of finite size quantum Hall bilayers on a sphere seem to infer a paired CF phase of the l ¼ −1 interlayer paired state at ν ¼ [31,32]. This l ¼ −1 state was found to be an exciton condensate in a very recent paper [33], which preserves the particle-hole symmetry of half-filled Landau levels.…”

Pairing instabilities of Dirac composite fermions

“…It is important to take into account the p-wave pairing [19] which was initially expressed in terms of ordinary HLR CF's. The picture based on the ordinary CF's does not have a clear answer for the lowest lying spectrum which appears nearly gapless (with small gap) or gapless when the system is put on a torus, while the topological p-wave pairing of ordinary fermions [33] would likely produce a clear gap of the order µ.…”

“…Furthermore, we find that the features, in particular low-energy spectrum, of the QHB at intermediate distances between the layers are better captured if we assume Dirac rather than HLR p-wave paired CF's at large distances (decoupled layers). Already at the effective field theory level, modeling the evolution with the distance between layers by Dirac CFs, we can detect the main feature of CF-composite boson (CB) mixed states [19,27]: the decrease in the number of CF's with decreasing distance.…”

“…In this system p-wave pairing between two kinds of non-relativistic Halperin-LeeRead (HLR) composite fermions at intermediate interlayer distances was proposed in Ref. [19], and, recently, this scenario was further substantiated by a detection of the topological signatures of the p-wave system in the torus geometry [20]. Therefore, it is natural to ask how this picture may be modified if we take into account the description by two Dirac CF's of the two half-filled LL monolayers, and consider their possible pairing.…”