Bilayer Quantum Hall Research Articles

Interlayer Tunneling in Counterflow Experiments on the Excitonic Condensate in Quantum Hall Bilayers

The effect of tunneling on the transport properties of quantum Hall double layers in the regime of the excitonic condensate at a total filling factor one is studied in counterflow experiments. If the tunnel current I is smaller than a critical I{C}, tunneling is large and is effectively shorting the two layers. For I>I{C} tunneling becomes negligible. Surprisingly, the transition between the two tunneling regimes has only a minor impact on the features of the filling-factor one state as observed in magnetotransport, but at currents exceeding I{C} the resistance along the layers increases rapidly.

Effect of disorder and electron-phonon interaction on interlayer tunneling current in quantum Hall bilayer

We study the transport properties of the quantum Hall bilayers systems looking closely at the effect that disorder and electron-phonon interaction have on the interlayer tunnelling current in the presence of an in-plane magnetic field $B_\parallel$. We find that it is important to take into account the effect of disorder and electron-phonon interactions in order to predict a finite current at a finite voltage when an in-plane magnetic field is present. We find a broadened resonant feature in the tunnelling current as a function of bias voltage, in qualitative agreement with experiments. We also find the broadening of this resonant feature due to electron-phonon coupling has a non-monotonic dependence on $B_\parallel$, related to the geometry of the double quantum well. We also compare this with the broadening effect due to spatial fluctuations of the tunnelling amplitude. We conclude that such static disorder provides only very weak broadening of the resonant feature in the experimental range.

Intrinsic Gap and Exciton Condensation in theνT=1Bilayer System

We investigate the quasiparticle excitation of the bilayer quantum Hall (QH) system at a total filling factor nu{T}=1 in the limit of negligible interlayer tunneling under a tilted magnetic field. We show that the intrinsic quasiparticle excitation is of purely pseudospin origin and solely governed by the inter- and intralayer electron interactions. A model based on exciton formation successfully explains the quantitative behavior of the quasiparticle excitation gap, demonstrating the existence of a link between the excitonic QH state and the composite fermion liquid. Our results provide a new insight into the nature of the phase transition between the two states.

Quantum Hall Exciton Condensation at Full Spin Polarization

Using Coulomb drag as a probe, we explore the excitonic phase transition in quantum Hall bilayers at nu(T) = 1 as a function of Zeeman energy E(Z). The critical layer separation (d/l)(c) for exciton condensation initially increases rapidly with E(Z), but then reaches a maximum and begins a gentle decline. At high E(Z), where both the excitonic phase at small d/l and the compressible phase at large d/l are fully spin polarized, we find that the width of the transition, as a function of d/l, is much larger than at small E(Z) and persists in the limit of zero temperature. We discuss these results in the context of two models in which the system contains a mixture of the two fluids.

Evidence of interlayer correlation in spin excitations of quantum Hall bilayers with negligible tunneling

Manifestations of interlayer excitonic coherence in a quantum Hall bilayer with negligible tunneling occur in low-lying spin excitations measured by inelastic light scattering. The observation of quasiparticle spin-flip excitations with energies below the Zeeman gap identifies a composite-fermion metal as the high-temperature phase of the quantum Hall coherent state. Spin-flip intensities enable the determination of a critical temperature for this transformation that is in general agreement with those obtained from charge transport experiments.

Skyrmion and bimeron excitations in bilayer quantum Hall systems

Charged excitations are topological solitons (skyrmions) in quantum Hall systems. They are CP 3 skyrmions in the bilayer system, where the underlying symmetry is SU(4). We present a microscopic formulation of CP 3 skyrmions in a system where the electron density is imbalanced between the two layers. A skyrmion is constructed by dressing a cloud of SU(4) isospins around an electron or a hole, and it carries the same charge as an electron or a hole at the filling factor ν = 1 . When the parallel magnetic field penetrates between the two layers, it deforms a skyrmion into a bimeron (a pair of merons). Each meron carries a fractional charge. We calculate the activation energy and show that it decreases rapidly as the parallel magnetic field increases near the balanced point.

Bilayer quantum Hall system atνt=1: Pseudospin models and in-plane magnetic field

We investigate two theoretical pseudomagnon-based models for a bilayer quantum Hall system (BQHS) at total filling factor $\nu_t = 1$. We find a unifying framework which elucidates the different approximations that are made. We also consider the effect of an in-plane magnetic field in BQHSs at $\nu_t = 1$, by deriving an equation for the ground state energy from the underlying microscopic physics. Although this equation is derived for small in-plane fields, its predictions agree with recent experimental findings at stronger in-plane fields, for low electron densities. We also take into account finite-temperature effects by means of a renormalisation group analysis, and find that they are small at the temperatures that were investigated experimentally.

Superconductivity of electron–hole pairs in a bilayer graphene system in a quantizing magnetic field

A state with spontaneous interlayer phase coherence in a bilayer quantum Hall system based on graphene is studied. This state can be regarded as a gas of superfluid electron–hole pairs whose components belong to different layers. A superfluid flow of such pairs is equivalent to two electric supercurrents in the layers. It is shown that in a graphene system a state with interlayer phase coherence arises if a definite unbalance of the filling factors of the Landau levels in neighboring layers is created. The temperature of the transition into a superfluid state, the maximum interlayer distance for which phase coherence is possible, and the critical values of the supercurrent are found. The advantages of using graphene systems instead of GaAs heterostructures to realize bilayer electron–hole superconductivity are discussed.

Vortex states of a disordered quantum Hall bilayer

We present and solve a model for the vortex configuration of a disordered quantum Hall bilayer in the limit of strong and smooth disorder. We argue that there is a characteristic disorder strength below which vortices will be rare and above which they proliferate. We predict that this can be observed tuning the electron density in a given sample. The ground state in the strong-disorder regime can be understood as an emulsion of vortex-antivortex crystals. Its signatures include a suppression of the spatial decay of counterflow currents. We find an increase of at least an order of magnitude in the length scale for this decay compared to a clean system. This provides a possible explanation of the apparent absence of leakage of counterflow currents through interlayer tunneling, even in experiments performed deep in the coherent phase where enhanced interlayer tunneling is observed.

Josephson vortex motion as a source for dissipation of superflow of e–h pairs inbilayers

It is shown that in a bilayer excitonic superconductor dissipative losses emerge undertransmission of the current from the source to the load. These losses are proportional to thesquare of the interlayer tunneling amplitude and are independent of the value of the inputcurrent. The case of a quantum Hall bilayer is considered. The bilayer may work as atransmission line if the input current exceeds a certain critical value. An input currenthigher than the critical one induces Josephson vortices in the bilayer. The difference inelectrochemical potentials is required to feed the load and it forces Josephsonvortices to move. The state becomes non-stationary which leads to dissipation.

Nonperturbative approach to the quantum Hall bilayer

We develop a nonperturbative approach to the quantum Hall bilayer (QHB) at $\ensuremath{\nu}=1$ using trial wave functions. We predict phases of the QHB for arbitrary distance $d$ and, our approach, in a dual picture, naturally introduces a new kind of quasiparticles---neutral fermions. Neutral fermion is a composite of two merons of the same vorticity and opposite charge. For small $d$ (i.e., in the superfluid phase), neutral fermions appear as dipoles. At larger $d$ dipoles dissociate into the phase of the two decoupled Fermi-liquid-like states. This scenario is relevant for the experimental situation where impurities lock charged merons. In a translation invariant (clean) system, continuous creation and annihilation of meron-antimeron pairs evolves the QHB toward a paired phase. The quantum fluctuations fix the form of the pairing function to $g(z)=1/{z}^{\ensuremath{\ast}}$. A part of the description of the paired phase is the two-dimensional superconductor i.e., BF Chern-Simons theory. The paired phase is not very distinct from the superfluid phase.

Trial wave functions forν=12+12quantum Hall bilayers

Quantum Hall bilayer systems at filling fractions near $\ensuremath{\nu}=\frac{1}{2}+\frac{1}{2}$ 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 wave functions. We consider two main classes of wave functions. In the first class, previously introduced in M\"oller et al. [Phys. Rev. Lett. 101, 176803 (2008)], we consider interlayer BCS pairing of two independent CF liquids. We find that these wave functions are exceedingly good for $d\ensuremath{\gtrsim}{\ensuremath{\ell}}_{0}$ with ${\ensuremath{\ell}}_{0}$ as the magnetic length. The second class of wave functions naturally follows the reasoning of Simon et al. [Phys. Rev. Lett. 91, 046803 (2003)] and generalizes the idea of pairing wave functions by allowing the CFs also to be replaced continuously by CBs. This generalization allows us to construct exceedingly good wave functions for interlayer spacings of $d\ensuremath{\lesssim}{\ensuremath{\ell}}_{0}$ as well. The accuracy of the wave functions discussed in this work, compared with exact diagonalization, approaches that of the celebrated Laughlin wave function.

Activation study of the pseudospin soliton in the v = 1 bilayer quantum Hall effect

We study thermal excitations of the pseudospin soliton phase in the bilayer quantum Hall (QH) state at total Landau level filling factor v = 1. Near the commensurate-incommensurate phase transition point in the bilayer v = 1 QH state, we have found anomalous magnetotransport phenomena, such as the magnetoresistance peak and its anisotropic transport, which are ascribed to the formation of the pseudospin soliton phase (A. Fukuda et al., Phys. Rev. Lett. 100, 016801 (2008)). In this work, we elaborately measured activation energy gap Δ of the bilayer v = 1 QH state. Δ shows a broad minimum in the pseudospin soliton phase between the commensurate and incommensurate phase. We suggest that the minimum in Δ is due to collective modes of the pseudospin solitons forming a lattice.

Magnetotransport study in the layer imbalanced v = 1 bilayer quantum Hall state

We carried out magnetotransport measurements of the charge imbalanced bilayer quantum Hall state (QHS) at the total Landau level filling factor ν = 1 under the titled magnetic fields. Changing the total electron densities nT and the layer imbalance parameter σ = (nf - nb)/(nf + nb), where nf(nb) indicates the density of the front (back) layer, we investigated magnetoresistance near the phase transition point between the charge transferable bilayer QHS and the 1/3+2/3 compound QHS at large in-plane magnetic fields B||. We measured the thermal activation energy Δ for various nT and θ, and constructed detailed phase diagram in the nT-θ plane at σ = 0.33, including commensurate(C)-like, incommensurate (IC)-like and the compound state. Results indicate that each transition between the compound QHS and the C-like or IC-like phases reflects the pseudospin symmetries.

First-Order Quantum Phase Transition of Excitons in Quantum Hall Bilayers

We show that the quantum phase transformation between compressible metallic and incompressible excitonic states in the coupled bilayers at total Landau level filling factor nuT=1 becomes discontinuous (first order) by impacts of different terms of the electron-electron interactions that prevail on weak residual disorder. The evidence is based on precise determinations of the excitonic order parameter by inelastic light scattering measurements close to the phase boundary. While there is marked softening of low-lying excitations, our experiments underpin the roles of competing order parameters linked to quasiparticle correlations in removing the divergence of quantum fluctuations.

Observation of an in-plane magnetic-field-driven phase transition in a quantum Hall system with SU(4) symmetry

In condensed matter physics, the study of electronic states with SU(N) symmetry has attracted considerable and growing attention in recent years, as systems with such a symmetry can often have a spontaneous symmetry-breaking effect giving rise to a novel ground state. For example, pseudospin quantum Hall ferromagnet of broken SU(2) symmetry has been realized by bringing two Landau levels close to degeneracy in a bilayer quantum Hall system. In the past several years, the exploration of collective states in other multi-component quantum Hall systems has emerged. Here we show the conventional pseudospin quantum Hall ferromagnetic states with broken SU(2) symmetry collapsed rapidly into an unexpected state with broken SU(4) symmetry, by in-plane magnetic field in a two-subband GaAs/AlGaAs two-dimensional electron system at filling factor around $\nu=4$. Within a narrow tilting range angle of 0.5 degrees, the activation energy increases as much as 12 K. While the origin of this puzzling observation remains to be exploited, we discuss the possibility of a long-sought pairing state of electrons with a four-fold degeneracy.

Quantum Hall to Insulator Transition in the Bilayer Quantum Hall Ferromagnet

We describe a phase transition of the bilayer quantum Hall ferromagnet at nu=1. In the presence of static disorder (modeled by a periodic potential), bosonic S=1/2 spinons undergo a superfluid-insulator transition while preserving ferromagnetism. The Mott insulating phase has an emergent U(1) photon, and the transition is between Higgs and Coulomb phases of this photon. Consequences for charge and counterflow conductivity and for interlayer tunneling conductance are discussed.

Paired Composite Fermion Phase of Quantum Hall Bilayers atν=12+12

We provide numerical evidence for composite fermion pairing in quantum Hall bilayer systems at filling nu=1/2+1/2 for intermediate spacing between the layers. We identify the phase as p_(x)+ip_(y) pairing, and construct high accuracy trial wave functions to describe the ground state on the sphere. For large distances between the layers, and for finite systems, a competing "Hund's rule" state, or composite fermion liquid, prevails for certain system sizes.

Theory of Activated Transport in Bilayer Quantum Hall Systems

We analyze the transport properties of bilayer quantum Hall systems at total filling factor nu=1 in drag geometries as a function of interlayer bias, in the limit where the disorder is sufficiently strong to unbind meron-antimeron pairs, the charged topological defects of the system. We compute the typical energy barrier for these objects to cross incompressible regions within the disordered system using a Hartree-Fock approach, and show how this leads to multiple activation energies when the system is biased. We then demonstrate using a bosonic Chern-Simons theory that in drag geometries current in a single layer directly leads to forces on only two of the four types of merons, inducing dissipation only in the drive layer. Dissipation in the drag layer results from interactions among the merons, resulting in very different temperature dependences for the drag and drive layers, in qualitative agreement with experiment.

Halperin(m,m′,n)Bilayer Quantum Hall States on Thin Cylinders

The Halperin (m,m',n) bilayer quantum Hall states are studied on thin cylinders. In this limit, charge-density-wave patterns emerge that are characteristic of the underlying quantum Hall state. The general patterns are worked out from a variant of the plasma analogy. Torus degeneracies are recovered, and for some important special cases a connection to well-known spin chain physics is made. By including interlayer tunneling, we also work out the critical behavior of a possible phase transition between the (331) state and the non-Abelian Moore-Read state in the thin cylinder limit.