Spin-Pseudospin Coherence and CP3^{3} Skyrmions in Bilayer Quantum Hall Ferromagnets

We analyze bilayer quantum Hall ferromagnets, whose underlying symmetry group is SU(4). Spin-pseudospin coherence develops spontaneously when the total electron density is low enough. Quasiparticles are CP^3 skyrmions. One skyrmion induces charge modulations on both of the two layers. At the filling factor$\nu =2/m$ one elementary excitation consists of a pair of skyrmions and its charge is $2e/m$. Recent experimental data due to Sawada et al. [Phys. Rev. Lett. {\bf 80}, 4534 (1998)] support this conclusion.Comment: 4 pages including 2 figures (published version

Interlayer Coherence in the ν=1\nu=1 and ν=2\nu=2 Bilayer Quantum Hall States

We have measured the Hall-plateau width and the activation energy of the bilayer quantum Hall (BLQH) states at the Landau-level filling factor $\nu=1$ and 2 by tilting the sample and simultaneously changing the electron density in each quantum well. The phase transition between the commensurate and incommensurate states are confirmed at $\nu =1$ and discovered at $\nu =2$. In particular, three different $\nu =2$ BLQH states are identified; the compound state, the coherent commensurate state, and the coherent incommensurate state.Comment: 4 pages including 5 figure

Noncommutative Geometry, Extended W(infty) Algebra and Grassmannian Solitons in Multicomponent Quantum Hall Systems

Noncommutative geometry governs the physics of quantum Hall (QH) effects. We introduce the Weyl ordering of the second quantized density operator to explore the dynamics of electrons in the lowest Landau level. We analyze QH systems made of $N$-component electrons at the integer filling factor $\nu=k\leq N$. The basic algebra is the SU(N)-extended W$_{\infty}$. A specific feature is that noncommutative geometry leads to a spontaneous development of SU(N) quantum coherence by generating the exchange Coulomb interaction. The effective Hamiltonian is the Grassmannian $G_{N,k}$ sigma model, and the dynamical field is the Grassmannian $G_{N,k}$ field, describing $k(N-k)$ complex Goldstone modes and one kind of topological solitons (Grassmannian solitons).Comment: 15 pages (no figures

Magnetotransport Study of the Canted Antiferromagnetic Phase in Bilayer ν=2\nu=2 Quantum Hall State

Magnetotransport properties are investigated in the bilayer quantum Hall state at the total filling factor $\nu=2$. We measured the activation energy elaborately as a function of the total electron density and the density difference between the two layers. Our experimental data demonstrate clearly the emergence of the canted antiferromagnetic (CAF) phase between the ferromagnetic phase and the spin-singlet phase. The stability of the CAF phase is discussed by the comparison between experimental results and theoretical calculations using a Hartree-Fock approximation and an exact diagonalization study. The data reveal also an intrinsic structure of the CAF phase divided into two regions according to the dominancy between the intralayer and interlayer correlations.Comment: 6 pages, 7 figure

Skyrmion ↔\leftrightarrow pseudoSkyrmion Transition in Bilayer Quantum Hall States at ν=1\nu =1

Bilayer quantum Hall states at $\nu =1$ have been demonstrated to possess a distinguished state with interlayer phase coherence. The state has both excitations of Skyrmion with spin and pseudoSkyrmion with pseudospin. We show that Skyrmion $\leftrightarrow$ pseudoSkyrmion transition arises in the state by changing imbalance between electron densities in both layers; PseudoSkyrmion is realized at balance point, while Skyrmion is realized at large imbalance. The transition can be seen by observing the dependence of activation energies on magnetic field parallel to the layers.Comment: 12 pages, no figure

Interlayer Exchange Interactions, SU(4) Soft Waves and Skyrmions in Bilayer Quantum Hall Ferromagnets

The Coulomb exchange interaction is the driving force for quantum coherence in quantum Hall systems. We construct a microscopic Landau-site Hamiltonian for the exchange interaction in bilayer quantum Hall ferromagnets, which is characterized by the SU(4) isospin structure. By taking a continuous limit, the Hamiltonian gives rise to the SU(4) nonlinear sigma model in the von-Neumann-lattice formulation. The ground-state energy is evaluated at filling factors $\nu =1,2,3,4$. It is shown at $\nu =1$ that there are 3 independent soft waves, where only one soft wave is responsible for the coherent tunneling of electrons between the two layers. It is also shown at $\nu =1$ that there are 3 independent skyrmion states apart from the translational degree of freedom. They are CP$^{3}$ skyrmions enjoying the spin-charge entanglement confined within the \LLL.Comment: 12 pages, 2 figure

The Study of Goldstone Modes in ν\nu=2 Bilayer Quantum Hall Systems

At the filling factor $\nu$=2, the bilayer quantum Hall system has three phases, the spin-ferromagnet phase, the spin singlet phase and the canted antiferromagnet (CAF) phase, depending on the relative strength between the Zeeman energy and interlayer tunneling energy. We present a systematic method to derive the effective Hamiltonian for the Goldstone modes in these three phases. We then investigate the dispersion relations and the coherence lengths of the Goldstone modes. To explore a possible emergence of the interlayer phase coherence, we analyze the dispersion relations in the zero tunneling energy limit. We find one gapless mode with the linear dispersion relation in the CAF phase.Comment: 13 pages, no figures. One reference is added. Typos correcte