Double-layer Quantum Hall Systems Research Articles

NUCLEAR-SPIN-BASED MEASUREMENTS OF QUANTUM HALL SYSTEMS

Nuclear magnetic resonance (NMR) is widely used in the physical, chemical, and biological sciences. However, conventional NMR techniques based on induction-detection have drawbacks of low-sensitivity and the need of a relatively large sample. It is not suitable to investigate single or double layers (or their nanostructure), which is essential in studying quantum Hall (QH) effects. In this presentation, I discussed a resistively-detected technique to overcome the low-sensitivity limitation of conventional NMR and its application to QH systems. Resistively-detected nuclear-spin-based measurements rely on enhanced interactions between electron and nuclear spins at the degenerate point of different electron-spin states. For example, at the ν = 2/3 degenerate point in a AlGaAs / GaAs system,1–3 nuclear-spin polarization far beyond the thermal equilibrium is generated using current flow (dynamic nuclear-spin polarization). Moreover, nuclear-spin polarization can be detected as enhanced resistance, which is proportional to the magnetization, Mz, of nuclear spins.2 It should be stressed that the special states of ν = 2/3 are needed for dynamic nuclear-spin polarization and Mz detection, but we can apply NMR spectrum and nuclear-spin relaxation (T1 time) measurements for any state we want to estimate. These nuclear-spin-based measurements were successfully applied to characterize QH systems, especially their electron-spin features, using single and double layer systems where characteristics are controlled electrically by the gate biases. For a single layer, we could clarify skyrmion,2 spin-polarization of composite fermion,4 and enhanced spin-orbit interactions in a strongly asymmetric confinement.5 Exciting phases, like a canted antiferromagnetic phase, were studied in a double layer QH system with a total filling factor of 2 (Refs. 6, 7). The low-frequency mode was sensitively detected by monitoring T1, reflecting correlated electron spin features.7 The clear observations of the characteristics, which are difficult to detect in conventional transport and optical measurements, make nuclear-spin-based measurement combined with resistance-detection a versatile and powerful tool for studying QH physics. Possible extensions of such measurements to semiconductor nanosystems were also discussed. The experiments discussed here were mainly carried out at NTT Basic Research Laboratories in collaboration with K. Muraki, N. Kumada, K. Takashina, K. Hashimoto, S. Watanabe and G. Yusa. Note from Publisher: This article contains the abstract only.

Directed transport in quantum Hall bilayers

The pseudo-spin model for double layer quantum Hall system with total landau level filling factor $\nu=1$ is discussed. Unlike the "traditional" one where interlayer voltage enters as static magnetic field along pseudo- spin hard axis, in our model we consider applied interlayer voltage as a frequency of precessing pseudo-magnetic field lying into the easy plane. It is shown that a Landau-Lifshitz equation for the considered pseudo magnetic system well describes existing experimental data. Besides that, the mentioned model predicts novel directed intra-layer transport phenomenon in the system: unidirectional intra-layer energy transport is realized due to interlayer voltage induced motion of topological kinks. This effect could be observed experimentally detecting counter-propagating intra-layer inhomogeneous charge currents which are proportional to the interlayer voltage and total topological charge of the pseudo-spin system.

Goldstone mode kink-solitons in double layer quantum Hall systems

It is shown that in charge unbalanced double layer quantum Hall system with zero tunneling pseudospin Goldstone mode excitations form moving kink-soliton in weakly nonlinear limit. This charge-density localization moves with a velocity of gapless linear spin-wave mode and could be easily observed experimentally. We claim that mentioned Goldstone mode kink-solitons define diffusionless charge transport properties in double layer quantum Hall systems.

Rippled state of double-layer quantum Hall systems

The incommensurate phase of a bilayer quantum Hall state is found to have a ``rippled'' dipole charge density whenever the layers are unbalanced. This tunable dipole-density-wave instability could be detected by sensitive capacitance measurements and by anisotropic transport. We demonstrate this explicitly by carrying out a Hartree-Fock calculation of the layer densities and capacitance for a double-layer quantum Hall state at a total filling factor of 1.

Thermodynamics of double-layer quantum Hall systems

In this paper we apply the exact solution of the sine-Gordon model to describe thermodynamic properties of the soliton liquid in the incommensurate phase of the double-layer quantum Hall systems. In this way we include thermal fluctuations and extend to finite temperatures the results obtained by C. B. Hanna, A. H. MacDonald, and S. M. Girvin [Phys. Rev. B 63, 125305 (2001)]. In addition we calculate the specific heat of the system. While the results obtained for the sine-Gordon model are available in a temperature interval ${(0,T}_{c}),$ where ${T}_{c}=8\ensuremath{\pi}{\ensuremath{\rho}}_{s},$ ${\ensuremath{\rho}}_{s}$ the pseudospin stiffness, they can be applied in the bilayer system up to temperatures $3{T}_{\mathrm{BKT}},$ where ${T}_{\mathrm{BKT}}=\ensuremath{\pi}{\ensuremath{\rho}}_{s}/2$ is the vortex-mediated Berezinskii-Kosterlitz-Thouless transition temperature. Above this temperature the operators $\mathrm{cos}\ensuremath{\beta}\ensuremath{\varphi}$ and $\mathrm{cos}(2\ensuremath{\pi}\ensuremath{\vartheta}/\ensuremath{\beta})$ are both relevant and the system is in a phase with coexisting order parameters. $\ensuremath{\vartheta}$ is the dual field of $\ensuremath{\varphi}$ and $\ensuremath{\beta}$ is the sine-Gordon coupling constant. We provide numerical estimates for thermodynamic quantities for the range of parameters relevant for GaAs.

Electromagnetic characteristics and effective gauge theory of double-layer quantum Hall systems

The electromagnetic characteristics of double-layer quantum Hall systems are studied, with projection to the lowest Landau level taken into account and intra-Landau-level collective excitations treated in the single-mode approximation. It is pointed out that dipole-active excitations, both elementary and collective, govern the long-wavelength features of quantum Hall systems. In particular, the presence of the dipole-active interlayer out-of-phase collective excitations, inherent to double-layer systems, modifies the leading O(k) and O(k^{2}) long-wavelength characteristics (i.e., the transport properties and characteristic scale) of the double-layer quantum Hall states substantially. We apply bosonization techniques and construct from such electromagnetic characteristics an effective theory, which consists of three vector fields representing the three dipole-active modes, one interlayer collective mode and two inter-Landau-level cyclotron modes. This effective theory properly incorporates the spectrum of collective excitations on the right scale of the Coulomb energy and, in addition, accommodates the favorable transport properties of the standard Chern-Simons theories.

On gauge invariance of noncommutative Chern–Simons theories

Motivated by possible applications to condensed matter systems, in this paper we construct U( N) noncommutative Chern–Simons (NCCS) action for a disc and for a double-layer geometry, respectively. In both cases, gauge invariance severely constrains the form of the NCCS action. In the first case, it is necessary to introduce a group-valued boson field with a nonlocal chiral boundary action, whose gauge variation cancels that of the bulk action. In the second case, the coefficient matrix K in the double U( N) NCCS action is restricted to be of the form K=k 1 1 1 1 with integer k. We suggest that this double NCCS theory with U(1) gauge group describes the so-called Halperin ( kkk) state in a double-layer quantum Hall system. Possible physical consequences are addressed.

Solitons in polarized double-layer quantum Hall systems

A new manifestation of interlayer coherence in strongly polarized double-layer quantum Hall systems with total filling factor $\ensuremath{\nu}=1$ in the presence of a small or zero tunneling is theoretically predicted. It is shown that moving (for small tunneling) and spatially localized (for zero tunneling) stable pseudospin solitons develop which could be interpreted as mobile or static charge-density excitations. The possibility of their experimental observation is also discussed.

Dynamics of quantum Hall stripes in double-quantum-well systems

The collective modes of stripes in double layer quantum Hall systems are computed using the time-dependent Hartree-Fock approximation. It is found that, when the system possesses spontaneous interlayer coherence, there are two gapless modes, one a phonon associated with broken translational invariance, the other a pseudospin-wave associated with a broken U(1) symmetry. For large layer separations the modes disperse weakly for wavevectors perpendicular to the stripe orientation, indicating the system becomes akin to an array of weakly coupled one-dimensional XY systems. At higher wavevectors the collective modes develop a roton minimum associated with a transition out of the coherent state with further increasing layer separation. A spin wave model of the system is developed, and it is shown that the collective modes may be described as those of a system with helimagnetic ordering.

Incommensurate ground state of double-layer quantum Hall systems

Double-layer quantum Hall systems possess interlayer phase coherence at sufficiently small layer separations, even without interlayer tunneling. When interlayer tunneling is present, application of a sufficiently strong in-plane magnetic field $B_\parallel > B_c$ drives a commensurate-incommensurate (CI) transition to an incommensurate soliton-lattice (SL) state. We calculate the Hartree-Fock ground-state energy of the SL state for all values of $B_\parallel$ within a gradient approximation, and use it to obtain the anisotropic SL stiffness, the Kosterlitz-Thouless melting temperature for the SL, and the SL magnetization. The in-plane differential magnetic susceptibility diverges as $(B_\parallel - B_c)^{-1}$ when the CI transition is approached from the SL state.

Interaction-induced localization-delocalization transition in the double-layer quantum Hall system

We report on numerical studies of the energy spectrum and the localization properties in the double-layer quantum Hall system at $\ensuremath{\nu}=1.$ The Coulomb interaction is treated by the Hartree-Fock approximation, and the localization properties in the presence of disorder are studied by evaluating participation ratios for the Hartree-Fock eigenfunctions. We show that the extended states seem to exist only near each center of the two subbands split by the exchange-enhanced energy gap. It is also shown that the self-consistent orbitals whose energies are close to the Fermi energy appear to become extended together with the reduction in the energy gap as the layer separation increases. The collapse of the energy gap expected from our results is consistent with the incompressible-compressible transition observed in recent experiments, and the change of the localization properties near the Fermi energy can explain the disappearance of the quantum Hall effect for large layer separations very well.

Stripes in quantum Hall double-layer systems

We present results of a study of double layer quantum Hall systems in which each layer has a high-index Landau level that is half-filled. Hartree-Fock calculations indicate that, above a critical layer separation, the system becomes unstable to the formation of a unidirectional coherent charge density wave (UCCDW), which is related to stripe states in single layer systems. The UCCDW state supports a quantized Hall effect when there is tunneling between layers, and is {\it always} stable against formation of an isotropic Wigner crystal for Landau indices $N \ge 1$. The state does become unstable to the formation of modulations within the stripes at large enough layer separation. The UCCDW state supports low-energy modes associated with interlayer coherence. The coherence allows the formation of charged soliton excitations, which become gapless in the limit of vanishing tunneling. We argue that this may result in a novel {\it ``critical Hall state''}, characterized by a power law $I-V$ in tunneling experiments.

Erratum: Quantum Dynamics of Pseudospin Solitons in Double-Layer Quantum Hall Systems [Phys. Rev. Lett. 83, 1411 (1999)

Pseudospin solitons in double-layer quantum Hall systems can be introduced by a magnetic field component coplanar with the electrons and can be pinned by applying voltages to external gates. We estimate the temperature below which depinning occurs predominantly via tunneling and calculate low-temperature depinning rates for realistic geometries. We discuss the local changes in charge and current densities and in spectral functions that can be used to detect solitons and observe their temporal evolution.

Quantum phase transitions in antiferromagnets and superfluids

We present a general introduction to the non-zero temperature dynamic and transport properties of low-dimensional systems near a quantum phase transition. Basic results are reviewed in the context of experiments on the spin-ladder compounds, insulating two-dimensional antiferromagnets, and double-layer quantum Hall systems. Recent large N computations on an extended t– J model (Phys. Rev. Lett. 83 (1999) 3916) motivate a global scenario of the quantum phases and transitions in the high-temperature superconductors, and connections are made to numerous experiments.

Order parameter suppression in double layer quantum Hall ferromagnets

Double-layer quantum Hall systems at Landau level filling factor ν=1 have a broken symmetry ground state with spontaneous interlayer phase coherence and a gap between symmetric and antisymmetric subbands in the absence of interlayer tunneling. We examine the influence of quantum fluctuations on the spectral function of the symmetric Green's function, probed in optical absorption experiments. We find that as the maximum layer separation at which the ν=1 quantum Hall effect occurs is approached, absorption in the lowest Landau level grows in strength. Detailed line shapes for this absorption are evaluated and related to features in the system's collective excitation spectrum.

Quantum Hall bilayers and the chiral sine-Gordon equation

The edge state theory of a class of symmetric double-layer quantum Hall systems with interlayer electron tunneling reduces to the sum of a free field theory and a field theory of a chiral Bose field with a self-interaction of the sine-Gordon form. We argue that the perturbative renormalization group flow of this chiral sine-Gordon theory is distinct from the standard (non-chiral) sine-Gordon theory, contrary to a previous assertion by Renn, and that the theory is manifestly sensible only at a discrete set of values of the inverse period of the cosine interaction ( β ̂ ). We obtain exact solutions for the spectra and correlation functions of the chiral sine-Gordon theory at the two values of β ̂ at which electron tunneling in bilayers is not irrelevant. Of these, the marginal case ( β ̂ 2=4 ) is of greatest interest: the spectrum of the interacting theory is that of two Majorana fermions with different, dynamically generated, velocities. For the experimentally observed bilayer 331 state at filling factor 1/2, this implies the trifurcation of electrons added to the edge. We also present a method for fermionizing the theory at the discrete points ( β ̂ 2∈ Z + ) by the introduction of auxiliary degrees of freedom that could prove useful in other problems involving quantum Hall multi-layers.

Spin mapping, phase diagram, and collective modes in double-layer quantum Hall systems atν=2

An exact spin mapping is identified to simplify the recently proposed hard-core boson description (Demler and Das Sarma, Phys. Rev. Lett., to be published) of the bilayer quantum Hall system at filling factor 2. The effective spin model describes an easy-plane ferromagnet subject to an external Zeeman field. The phase diagram of this effective model is determined exactly and found to agree with the approximate calculation of Demler and Das Sarma, while the Goldstone-mode spectrum, order parameter stiffness and Kosterlitz-Thouless temperature in the canted antiferromagnetic phase are computed approximately.

Quantum Dynamics of Pseudospin Solitons in Double-Layer Quantum Hall Systems

Pseudospin solitons in double-layer quantum Hall systems can be introduced by a magnetic field component coplanar with the electrons and can be pinned by applying voltages to external gates. We estimate the temperature below which depinning occurs predominantly via tunneling and calculate low-temperature depinning rates for realistic geometries. We discuss the local changes in charge and current densities and in spectral functions that can be used to detect solitons and observe their temporal evolution.

Universal relaxational dynamics near two-dimensional quantum critical points

We describe the nonzero temperature (T), low frequency (\omega) dynamics of the order parameter near quantum critical points in two spatial dimensions (d), with a special focus on the regime \hbar\omega << k_B T. For the case of a `relativistic', O(n)-symmetric, bosonic quantum field theory we show that, for small \epsilon=3-d, the dynamics is described by an effective classical model of waves with a quartic interaction. We provide analytical and numerical analyses of the classical wave model directly in d=2. We describe the crossover from the finite frequency, "amplitude fluctuation", gapped quasiparticle mode in the quantum paramagnet (or Mott insulator), to the zero frequency "phase" (n >= 2) or "domain wall" (n=1) relaxation mode near the ordered state. For static properties, we show how a surprising, duality-like transformation allows an exact treatment of the strong-coupling limit for all n. For n=2, we compute the universal T dependence of the superfluid density below the Kosterlitz-Thouless temperature, and discuss implications for the high temperature superconductors. For n=3, our computations of the dynamic structure factor relate to neutron scattering experiments on La_{1.85}Sr_{0.15}CuO_4, and to light scattering experiments on double layer quantum Hall systems. We expect that closely related effective classical wave models will apply also to other quantum critical points in d=2.

Interaction of a quantum Hall system with waveguide elastic modes

An interaction of non-uniform plane elastic modes of the waveguide type with monolayer and double-layer quantum Hall systems is considered. It is shown, that unlike the case of the surface acoustic wave propagation, the restriction on maximal values of the wave vectors for which the velocity shift can be observed experimentally does not take place for the waveguide modes. In case of study of incompressible fractional quantum Hall states the effect can be used for measuring a dependence of the effective magnetic length on the filling factor and for observing phase transitions in double-layer system under the interlayer distance variation