Trial Wavefunctions for \nu = 1/2 + 1/2 Quantum Hall Bilayers

TL;DR

This paper develops and tests trial wavefunctions to describe the intermediate phases of quantum Hall bilayers at /2 + 1/2, bridging the known composite fermion and composite boson regimes.

Contribution

It introduces and evaluates new variational wavefunctions based on interlayer pairing and CF-CB interpolation, achieving high accuracy across different layer separations.

Findings

Wavefunctions are highly accurate for large layer separation (d >~ ).

Wavefunctions also perform well for small layer separation (d <~ ).

Accuracy approaches that of the Laughlin wavefunction.

Abstract

Quantum Hall bilayer systems at filling fractions near \nu = 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 by Moller et al. [PRL {\bf 101}, 176803 (2008)], we consider interlayer BCS pairing of two independent CF liquids. We find that these wavefunctions are exceedingly good for d >~ \ell_0 with \ell_0 the magnetic length. The second class of wavefunctions naturally follows the reasoning of Simon et al. [PRL {\bf 91}, 046803 (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 <~ \ell_0, as well. The accuracy of the wavefunctions discussed in this work, compared with exact diagonalization, approaches that of the celebrated Laughlin wavefunction.