Abstract:
An improved composite-boson theory of quantum Hall ferromagnets is formulated both for the monolayer and bilayer systems. In this scheme the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. Skyrmions are charged excitations confined to the lowest Landau level. By evaluating the excitation energy of one skyrmion in the interlayer-coherent phase it is shown that the bilayer QH state becomes stabler as the interlayer density difference becomes larger.

Abstract:
A field theory of quantum Hall effects is constructed based on the \CB picture. It is tightly related with the microscopic wave-function theory. The characteristic feature is that the field operator describes solely the physical degrees of freedom representing the deviation from the Laughlin state. It presents a powerful tool to analyze excited states within the \LLL. It is shown that all excitations are nonlocal topological solitons in the spinless quantum Hall system. On the other hand, in the presence of the spin degree of freedom it is shown that a quantum coherence develops spontaneously, where excitations include a Goldstone mode besides nonlocal topological solitons. Solitons are vortices and Skyrmions carrying the U(1) and SU(2) topological charges, respectively. Their classical configurations are derived from their microscopic wave functions. The Skyrmion appears merely as a low-energy excitation within the \LLL and not as a solution of the effective nonlinear sigma model. We use it as a consistency check of the Skyrmion theory that the Skyrmion is reduced to the vortex in the vanishing limit of the Skyrmion size. We evaluate the activation energy of one Skyrmion and compare it with experimental data.

Abstract:
We propose an improved composite-boson theory of quantum Hall ferromagnets, where the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. In this scheme skyrmions appear merely as generic excitations confined in the lowest Landau level. We evaluate the excitation energy of one skyrmion. Our theoretical estimation accounts for the activation-energy data due to Schmeller et al. remarkably well.

Abstract:
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.

Abstract:
We analyze the bilayer quantum Hall (QH) system by mapping it to the monolayer QH system with spin degrees of freedom. By this mapping the tunneling interaction term is identified with the Zeeman term. We clarify the mechanism of a spontaneous development of quantum coherence based on the Chern-Simons gauge theory with the lowest-Landau-Level projection taken into account. The symmetry group is found to be W_infty*SU(2), which says that the spin rotation affects the total electron density nearby. Using it extensively we construct the Landau-Ginzburg theory of the coherent mode. Skyrmion excitations are topological solitons in this coherent mode. We point out that they are detectable by measuring the Hall current distribution.

Abstract:
An improved composite-boson theory of quantum Hall ferromagnets is proposed. It is tightly related with the microscopic wave-function theory. The characteristic feature is that the field operator describes solely the physical degrees of freedom representing the deviation from the ground state. It presents a powerful tool to analyze excited states within the \LLLd. Excitations include a Goldstone mode and nonlocal topological solitons. Solitons are vortices and Skyrmions carrying the U(1) and SU(2) topological charges, respectively. Their classical configurations are derived from their microscopic wave functions. The activation energy of one Skyrmion is estimated, which explains experimental data remarkably well.

Abstract:
The bilayer 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 SU(4). At $\nu =1$ the QH state is a charge-transferable state between the two layers and the SU(4) isospin coherence develops spontaneously. Quasiparticles are isospin textures to be identified with 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 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 Murphy et al. and Sawada et al. on the activation energy anomaly induced by applying parallel magnetic field.

Abstract:
We make a semiclassical analysis of thermal pair creations of quasiparticles at various filling factors in quantum Hall systems. It is argued that the gap energy is reduced considerably by the Coulomb potential made by impurities. It is also shown that a tunneling process becomes important at low temperature and at strong magnetic field. We fit typical experimental data excellently based on our semiclassical results of the gap energy.

Abstract:
At the filling factor $\nu=2$ the bilayer quantum Hall system has three phases, the ferromagnetic phase (spin phase), the spin singlet phase (ppin phase) and the canted antiferromagnetic phase. We analyze soft waves and quasiparticle excitations in the spin and ppin phases. It is shown that the dynamic field is the Grassmannian G$_{4,2}$ field carrying four complex degrees of freedom. In each phase there are four complex soft waves (pseudo-Goldstone modes) and one kind of skyrmion excitations (G$_{4,2}$ skyrmions) flipping either spins or pseudospins coherently. An intriguing property is that a quasiparticle is a G$_{4,2}$ skyrmion essentially consisting of two CP$^{3}$ skyrmions and thus possesses charge $2e$.

Abstract:
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.