Bilayer Quantum Hall Systems Research Articles

Quantum Hall liquid on a noncommutative superplane

Supersymmetric quantum Hall liquids are constructed on a noncommutative superplane. We explore a supersymmetric formalism of the Landau problem. In the lowest Landau level, there appear spin-less bosonic states and spin-1/2 down fermionic states, which exhibit a super-chiral property. It is shown the Laughlin wavefunction and topological excitations have their superpartners. Similarities between supersymmetric quantum Hall systems and bilayer quantum Hall systems are discussed.

Anisotropic magnetotransport around the ν=1 bilayer quantum Hall state

An anisotropic magnetotransport that depends on a direction of an in-plane magnetic field was investigated in a bilayer quantum Hall system. We have found that the longitudinal resistance around the bilayer ν=1 quantum Hall state strongly varies when we changed the relative angle between the current and the in-plane field. Indeed, the anisotropy becomes remarkable at the phase transition point between the commensurate and incommensurate states. This result suggests that a unidirectional state appears around the transition.

Quantum Hall effect in bilayer systems and the noncommutative plane: A toy model approach

We have presented a quantum mechanical toy model for the study of Coulomb interactions in Quantum Hall (QH) system. Inclusion of Coulomb interaction is essential for the study of bilayer QH system and our model can simulate it, in the compound state, in a perturbative framework. We also show that in the noncommutative plane, the Coulomb interaction is modified at a higher order in the noncommutativity parameter θ, and only if θ varies from layer to layer in the QH system.

Spin-flip excitations in bilayer quantum Hall ferromagnets

Bilayer quantum Hall systems at ν=1 are believed to have a ground state with spontaneous spin-polarization and spontaneous interlayer phase coherence. In this paper, we address the spectrum of spin-flip collective excitations using a generalized lattice spin model that appeals to the quantum Hall gap to justify neglect of charge fluctuations. We find that the long wavelength spin-flip excitation spectrum consists of the global Larmor spin-wave mode and a higher energy mode in which spin-waves in the two-layers are out of phase. We address the dependence of the energy splitting of the two modes on quantum fluctuations in the bilayer ground state.

HARTREE–FOCK–BOGOLIUBOV STUDIES OF BILAYER ν = 2 QUANTUM HALL SYSTEMS

Excitation spectra in bilayer quantum Hall systems at total Landau-level filling ν = 2 are studied by the Hartree–Fock–Bogoliubov (HFB) approximation. The systems have the spin degrees of freedom in addition to the layer degrees of freedom described in terms of pseudospin. On the excitation spectrum from the spin-singlet and pseudospin-polarized ground state, this approximation fully preserves the spin rotational symmetry and thus can give both spin-triplet and spin-singlet excitations systematically. It is also found that the ground state is pseudospin squeezed because of pseudospin correlations and that the HFB approximation can describe ground-state properties better than other approximations.

Vortices, Tunneling, and Deconfinement in Bilayer Quantum Hall Excitonic Superfluid

The physics of vortices, instantons, and deconfinement is studied for layered superfluids in connection to bilayer quantum Hall systems at filling fraction nu = 1. We develop an effective gauge theory taking into account both vortices and instantons induced by interlayer tunneling. The renormalization group flow of the gauge charge and the instanton fugacity shows that the coupling of the gauge field to vortex matter produces a continuous transition between the confining phase of free instantons and condensed vortices and a deconfined gapless superfluid where magnetic charges are bound into dipoles. The interlayer tunneling conductance and the layer-imbalance induced inhomogeneous exciton condensate are discussed in connection to experiments.

Tunneling between two-dimensional electron systems in a high magnetic field: Role of interlayer interactions

We calculate the tunneling current for a bilayer quantum Hall system in the interlayer incoherent regime. In order to capture the strong correlation effects we model the layers as two Wigner crystals coupled through interlayer Coulomb interactions, treated in the continuum limit. By generalizing previous work by Johansson and Kinaret (JK), we are able to study the effect of the low energy out-of-phase magnetophonon modes on the electron ``shake-up'' which occurs during a tunneling event. We find the tunneling current peak value to scale with the magnetic field as found by JK; however, we find a different scaling of the peak value with the interlayer separation, which agrees with the measurements by Eisenstein et al. [Phys. Rev. Lett. 74, 1419 (1995)].

Ground-state structure inν=2bilayer quantum Hall systems

We investigate the ground-state structure of the bilayer quantum Hall system at the filling factor $\nu =2$. Making an exact analysis of the ground state in the SU(4)-invariant limit, we include all other interactions as small perturbation. We carry out analytic calculations and construct phase diagrams for nonzero values of the Zeeman, tunneling and bias interactions. In particular we examine carefully how the phase transition occurs by applying the bias voltage and inducing a density imbalance between the two layers. We compare our theoretical result with the experimental data due to Sawada et al. based on the phase diagram in the $\sigma_{0}$-$\rho_{0}$ plane, where $\rho _{0}$ and $\sigma_{0}$ are the total electron density and the density difference between the two layers, respectively.

Broken symmetry, excitons, gapless modes, and topological excitations in trilayer quantum Hall systems

We study the interlayer coherent incompressible phase in Trilayer Quantum Hall systems (TLQH) at total filling factor $ \nu_{T}=1 $ from three approaches: Mutual Composite Fermion (MCF), Composite Boson (CB) and wavefunction approach. Just like in Bilayer Quantum Hall system, CB approach is superior than MCF approach in studying TLQH with broken symmetry. The Hall and Hall drag resistivities are found to be quantized at $ h/e^{2} $. Two neutral gapless modes with linear dispersion relations are identified and the ratio of the two velocities is close to $ \sqrt{3} $. The novel excitation spectra are classified into two classes: Charge neutral bosonic 2-body bound states and Charge $ \pm 1 $ fermionic 3-body bound states. In general, there are two 2-body Kosterlize-Thouless (KT) transition temperatures and one 3-body KT transition. The Charge $ \pm 1 $ 3-body fermionic bound states may be the main dissipation source of transport measurements. The broken symmetry in terms of $ SU(3) $ algebra is studied. The structure of excitons and their flowing patterns are given. The coupling between the two Goldstone modes may lead to the broadening in the zero-bias peak in the interlayer correlated tunnelings of the TLQH. Several interesting features unique to TLQH are outlined. Limitations of the CB approach are also pointed out.

Trial wave function approach to bilayer quantum Hall systems

We study the properties of some known trial wave functions in bilayer quantum Hall systems at the total filling factor ${\ensuremath{\nu}}_{T}=1$. In particular, we find that the properties of a meron wave function and a natural ``quasihole'' wave function are dramatically different due to the broken symmetry and the associated Goldstone mode in the bulk. Although the (smallest) meron has localized charge $1∕2$ and logarithmically divergent energy, the charge of the quasihole excitation extends over the whole system and its energy diverges linearly with the area of the system. This indicates that the natural quasihole wave function is not a good trial wave function for excitations. It also shows that the energy of the naive candidate for a pair of meron wave functions written down previously increases quadratically instead of logarithmically as their separation increases. Our results indicate that qualitatively good trial wave functions for the ground state and the excitations of the interlayer coherent bilayer quantum Hall system at finite $d$ are still not available and searching for them remains an important open problem.

ANISOTROPIC TRANSPORT ON THE ν=1 BILAYER QUANTUM HALL SYSTEM UNDER TILTED MAGNETIC FIELD

We measured an anisotropic magnetotransport that depends on directions of an in-plane field in a bilayer quantum Hall system. We found that the longitudinal resistance near the bilayer ν=1 quantum Hall state strongly varies when we changed an relative angle between the current and the in-plane field. It is a phenomenon peculiar to the bilayer ν=1 quantum Hall state, because this phenomenon does not appear in a monolayer system.

Gap Evolution in ν=1/2 Bilayer Quantum Hall Systems

Fractional quantum Hall states in bilayer system at total filling fraction $\nu=1/2$ are examined numerically under some ranges of the layer separation and interlayer tunneling. It is shown that the ground state changes continuously from two-component state to one-component state as the interlayer tunneling rate is increased, while the lowest excited state changes discontinuously. This fact explains observed unusual behavior of the activation energy which reveals upward cusp as a function of interlayer tunneling. Some trial wave functions for the ground state and quasihole states are inspected.

Global phase diagram ofν=2quantum Hall bilayers in tilted magnetic fields

We consider a bilayer quantum Hall system at total filling fraction $\ensuremath{\nu}=2$ in tilted magnetic field allowing for charge imbalance as well as tunneling between the two layers. Using an ``unrestricted Hartree Fock,'' previously discussed by Burkov and MacDonald [Phys. Rev. B 66, 115323 (2002)], we examine the zero-temperature global phase diagrams that would be accessed experimentally by changing the in-plane field and the bias voltage between the layers while keeping the tunneling between the two layers fixed. In accordance with previous work, we find symmetric and ferromagnetic phases as well as a first-order transition between two canted phases with spontaneously broken U(1) symmetry. We find that these two canted phases are topologically connected in the phase diagram and, reminiscent of a first-order liquid-gas transition, the first-order transition line between these two phases ends in a quantum critical point. We develop a physical picture of these two phases and describe in detail the physics of the transition.

SU(4)skyrmions and activation energy anomaly in bilayer quantum Hall systems

The bilayer quantum Hall (QH) system has four energy levels in the lowest Landau level, corresponding to the layer and spin degrees of freedom. We investigate the system in the regime where all four levels are nearly degenerate and equally active. The underlying group structure is $\mathrm{SU}(4)$. At $\ensuremath{\nu}=1$ the QH state is a charge-transferable state between the two layers and the $\mathrm{SU}(4)$ isospin coherence develops spontaneously. Quasiparticles are isospin textures to be identified with $\mathrm{SU}(4)$ skyrmions. The skyrmion energy consists of the Coulomb energy, the Zeeman energy and the pseudo-Zeeman energy. The Coulomb energy consists of the self-energy, the capacitance energy and the exchange energy. At the balanced point only pseudospins are excited unless the tunneling gap is too large. Then, the $\mathrm{SU}(4)$ skyrmion evolves continuously from the pseudospin-skyrmion limit into the spin-skyrmion limit as the system is transformed from the balanced point to the monolayer point by controlling the bias voltage. Our theoretical result explains quite well the experimental data due to Murphyet al. [S. Q. Murphy, J. P. Eisenstein, G. S. Boebinger, L. N. Pfeiffer, and K. W. West, Phys. Rev. Lett. 72, 728 (1994)] and Sawada et al. [A. Sawada, D. Terasawa, N. Kumada, M. Morino, K. Tagashira, Z. F. Ezawa, K. Muraki, T. Saku, and Y. Hirayama, Physica E 18, 118 (2003); D. Terasawa, M. Morino, K. Nakada, S. Kozumi, A. Sawada, Z. F. Ezawa, N. Kumada, K. Muraki, T. Saku, and Y. Hirayama, Physica E 22, 52 (2004)] on the activation energy anomaly induced by applying parallel magnetic field.

Status of the Fermi surface in mixed composite-boson–composite-fermion quantum Hall states

We argue that the naively expected singularities of the Fermi surface, in the mixed composite boson-composite fermion states proposed [S.H. Simon et al., Phys. Rev. Lett. 91, 046803 (2003)] for the evolution of $\ensuremath{\nu}=1$ bilayer quantum Hall system with distance, are obliterated. Our conclusion is based on a careful analysis of the momentum distribution in $\ensuremath{\nu}=\frac{1}{2}$ single-layer composite-fermion state. We point out to a possibility of the phenomenon hitherto unknown outside Kondo lattice systems when, in a translationally invariant system, Fermi-liquid-like portion of electrons enlarges its volume.

Tunneling, dissipation, and superfluid transition in quantum Hall bilayers.

We study bilayer quantum Hall systems at total Landau level filling factor nu=1 in the presence of interlayer tunneling and coupling to a dissipative normal fluid. Describing the dynamics of the interlayer phase by an effective quantum dissipative XY model, we show that there exists a critical dissipation sigma(c) set by the conductance of the normal fluid. For sigma>sigma(c), interlayer tunnel splitting drives the system to a nu=1 quantum Hall state. For sigma<sigma(c), interlayer tunneling is irrelevant at low temperatures; the system exhibits an excitonic superfluid transition to a collective quantum Hall state supported by spontaneous interlayer phase coherence. The resulting phase structure and the behavior of the in-plane and tunneling currents are studied in connection to experiments.

Collective transport in bilayer quantum Hall systems

Filling factor ν=1 incompressible states in ideal bilayer quantum Hall systems have spontaneous interlayer phase coherence and can be regarded either as easy-plane pseudospin ferromagnets or as condensates of excitons formed from electrons in one layer and holes in the other layer. In this paper we discuss efforts to achieve an understanding of the two different types of transport measurements (which we refer to as drag and tunneling experiments, respectively) that have been carried out in bilayer quantum Hall systems by the group of Jim Eisenstein at the California Institute of Technology. In a drag experiment, current is sent through one of the two-layers and the voltage drop is measured in the other layer. We will argue that the finding of these experiments that the voltage drop in the drag layer is different from that in the drive layer, is an experimental proof that these bilayers do not have quasi-long-range excitonic order. The property that at ν=1 the longitudinal drag voltage increases from near zero when spontaneous coherence is initially established, then falls back toward zero as it becomes well established, can be explained as a competition between the broken symmetry and the gap to which it gives rise. In the tunneling experiment, current is injected in one layer and removed from the other layer. The absence of quasi-long-range order likely explains the relatively small tunneling conductance per area found in the these measurements.

Excitation spectrum of bilayer ν=2 quantum Hall systems

Excitation spectra in bilayer quantum Hall systems at total Landau-level filling ν=2 are studied by the Hartree–Fock–Bogoliubov approximation. The systems have the spin degrees of freedom in addition to the layer degrees of freedom described in terms of pseudospin. On the excitation spectra from spin-unpolarized and pseudospin-polarized ground state, this approximation fully preserves the spin rotational symmetry and thus can give not only spin-triplet but also spin-singlet excitations systematically. It is also found that the ground-state properties are well described by this approximation.

Noise spectroscopy and interlayer phase coherence in bilayer quantum Hall systems.

Bilayer quantum Hall systems develop strong interlayer phase coherence when the distance between layers is comparable to the typical distance between electrons within a layer. The phase-coherent state has until now been investigated primarily via transport measurements. We argue here that interlayer current and charge-imbalance noise studies in these systems will be able to address some of the key experimental questions. We show that the characteristic frequency of current noise is that of the zero wave vector collective mode, which is sensitive to the degree of order in the system. Local electric potential noise measured in a plane above the bilayer system, on the other hand, is sensitive to finite-wave-vector collective modes and, hence, to the soft-magnetoroton picture of the order-disorder phase transition.

Spontaneous pseudospin spiral order in bilayer quantum Hall systems

Using exact diagonalization of bilayer quantum Hall systems at total filling factor $\nu_T=1$ in the torus geometry, we show that there is a new long-range interlayer phase coherence due to spontaneous pseudospin spiral order at interlayer distances larger than the critical value at which the pseudospin ferromagnetic order is destroyed. We emphasize the distinction between the interlayer phase coherence and the pseudospin ferromagnetic order.