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arXiv:1407.1528 · Europhysics Letters (EPL)

Quantum Hall bilayer as pseudospin magnet

Oleksandr Kyriienko, K. Wierschem, Pinaki Sengupta, Ivan Andreevich Shelykh

Published Mar 1, 2015• 4 citations
arXivHTMLPDF

Abstract

We revisit the physics of electron gas bilayers in the quantum Hall regime (M ac D onald A. and E isenstein J., Nature , 432 (2004) 691; E isenstein J., Science , 305 (2004) 950), where transport and tunneling measurements provided evidence of a superfluid phase being present in the system. Previously, this behavior was explained by the possible formation of a BEC of excitons in the half-filled electron bilayers, where empty states play the role of holes. We discuss the fundamental difficulties with this scenario, and propose an alternative approach based on a treatment of the system as a pseudospin magnet. We show that the experimentally observed tunneling peak can be linked to the XY ferromagnet (FM) to Ising antiferromagnet (AFM) phase transition of the S = 1/2 XXZ pseudospin model, driven by the change in total electron density. This transition is accompanied by a qualitative change in the nature of the low-energy spin wave dispersion from a gapless linear mode in the XY-FM phase to a gapped, quadratic mode in the Ising AFM phase.

DOI
10.1209/0295-5075/109/57003

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We revisit the physics of electron gas bilayers in the quantum Hall regime (M ac D onald A. and E isenstein J., Nature , 432 (2004) 691; E isenstein J., Science , 305 (2004) 950), where transport and tunneling measurements provided evidence of a superfluid phase being present in the system. Previously, this behavior was explained by the possible formation of a BEC of excitons in the half-filled electron bilayers, where empty states play the role of holes. We discuss the fundamental difficulties with this scenario, and propose an alternative approach based on a treatment of the system as a pseudospin magnet. We show that the experimentally observed tunneling peak can be linked to the XY ferromagnet (FM) to Ising antiferromagnet (AFM) phase transition of the S = 1/2 XXZ pseudospin model, driven by the change in total electron density. This transition is accompanied by a qualitative change in the nature of the low-energy spin wave dispersion from a gapless linear mode in the XY-FM phase to a gapped, quadratic mode in the Ising AFM phase.
We construct a mapped bilayer quantum Hall system to realize the proposal that two nearly flatbands have opposite Chern numbers. For the C = ±1 case, the two Landau levels of the bilayer experience opposite magnetic fields. We consider a mapped bilayer quantum Hall system at total filling ν t = 1 2 + 1 2 where the intralayer interaction is repulsive and the interlayer interaction is attractive. We take exact diagonalization (ED) calculations on a torus to study the phase transition when the separation distance d/lB is driven. The critical point at d c/lB = 0.68 is characterized by a collapse of degeneracy and a crossing of energy levels. In the region d/lB < d c/lB , the states of each level are highly degenerate. The pair-correlation function indicates electrons with opposite pseudo-spins are strong correlated at r = 0. We find an exciton stripe phase composed of bound pairs. The ferromagnetic ground state is destroyed by the strong effective attractive potential. An electron composite-Fermion (eCF) and a hole composite Fermion (hCF) are tightly bound. In the region d/lB > d c/lB , a crossover from the d → d c limit to the large d limit is observed. The electron and hole composite Fermion liquids (CFL) are realized by composite Fermions (CF) which attach opposite fluxes, respectively.
This paper reviews the authors' theoretical understanding for the quantum Hall anomalies recently observed at fractional fillings with even denominators, more particularly at filling 1/2, where the electron spins are still fully polarized. After a brief reminder of the basic experimental evidence dip of {rho}{sub xx}, lack of plateau in {rho}{sub xx}, temperature behavior, the author discusses the important role of electron-hole (e-h) symmetry at half-filling. In particular the two alternative possibilities of spontaneous e-h symmetry breaking or non-breaking are discussed along with their physical implications. Hartree-Fock charge density waves are presented as an explicit example of spontaneous e-h symmetry breaking. Next, several different scenarios are discussed for the ground state at half-filling. One, largely discussed in the experimental papers is that of Halperin, involving phase separation. Another is that of Fano et al. where the half-filling ground state is supposed to be incompressible and homogeneous, but deformable. Pursuing further the second scenario, numerical evidence from the recent work of Chen is presented, indicating incompressibility and deformability. This work also demonstrates a rather abrupt switching of short-range electron correlations. Just below half-filling, an electron is typically surrounded by six close-by electrons (like a triangular lattice).
We examine the quantum phase diagram of the fractional quantum Hall effect (FQHE) in the lowest two Landau levels in half-filled bilayer structures as a function of tunneling strength and layer separation, i.e., we revisit the lowest Landau-level filling factor 1/2 bilayer problem and make predictions involving bilayers in the half-filled second Landau level (i.e., filling factor 5/2). Using numerical exact diagonalization we investigate the important question of whether this system supports a FQHE described by the non-Abelian Moore-Read Pfaffian state in the strong-tunneling regime. In the lowest Landau level, we find that although, in principle, increasing (decreasing) tunneling strength (layer separation) could lead to a transition from the Abelian two-component Halperin 331 to non-Abelian one-component Moore-Read Pfaffian state, the FQHE excitation gap is relatively small in the lowest Landau level Pfaffian regime, and we establish that all so far observed FQHE states in half-filled lowest Landau level bilayers are most likely described by the Abelian Halperin 331 state. In the second Landau level we make the prediction that bilayer structures would manifest two distinct branches of incompressible FQHE corresponding to the Abelian 331 state (at moderate to low tunneling and large layer separation) and the non-Abelian Moore-Read Pfaffian state (at large tunneling and small layer separation). The observation of these two FQHE branches and the possible quantum phase transition between them will be compelling evidence supporting the existence of the non-Abelian Moore-Read Pfaffian state in the second Landau level. We discuss our results in the context of existing experiments and theoretical works.
We theoretically consider bilayers of two-dimensional (2D) electron gases as in semiconductor quantum wells, and investigate possible spontaneous symmetry breaking transitions at low carrier densities driven by interlayer Coulomb interactions. We use a self-consistent technique implementing mean-field truncations of the interacting four-fermion terms, and find a U(1) layer symmetry breaking transition at low carrier densities where the individual layer identities are lost leading to an effective pseudospin XY ferromagnet in the 2D plane. Our results validate earlier theoretical studies using simpler restricted Hartree-Fock techniques, and establish the pseudospin XY ferromagnet as a possible low-density symmetry broken phase of 2D bilayers.
We investigate the nature of the magnetic excitations of a bilayer single-orbital Hubbard model in the intermediate-coupling regime.This model exhibits a quantum phase transition (QPT) between a paramagnetic (PM) and an insulating antiferromagnetic (AFM) phase at a critical value of the coupling strength.By using the random phase approximation, we show that the QPT is continuous when the PM state is a band insulator and that the corresponding quantum critical point (QCP) arises from the condensation of preformed excitons.These low-energy excitons re-emerge on the other side of the QCP as the transverse and longitudinal modes of the AFM state.In particular, the longitudinal mode remains sharp for the model parameters relevant to Sr 3 Ir 2 O 7 because of the strong easy-axis anisotropy of this material.
We study the phase diagram of quantum Hall bilayer systems with total filing ν_{T}=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/l_{B}<1.8 (l_{B} 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 and (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 ν_{T}=1.