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Based on the Noether's theorem, we develop systematically and rigorously the spin-dependent formulation of the conservation laws. The effect of the electronic polarization due to the spin-orbit coupling is included in the Maxwell equations. The polarization is related to the antisymmetric components of spin current, and it provides a possibility to measure the spin current directly. The variances of spin and orbit angular momentum currents imply a torque on the "electric dipole" associated with the moving electron. The dependencies of the torque on the polarization and the force on the motions of spin-polarized electrons in a two-dimensional electron gas with the Rashba spin-orbit coupling are discussed.

Layered organic superconductors are on the verge of the Mott insulator. We use the Gutzwiller variational method to study a two-dimensional Hubbard model including a spin exchange coupling term as a minimal model for the compounds. The ground state is found to be a Gossamer superconductor at small on-site Coulomb repulsion U and an antiferromagnetic Mott insulator at large U, separated by a first order phase transition. Our theory is qualitatively consistent with major experiments reported in organic superconductors.

We present a general theory for the Fano resonance in Anderson impurity systems. It is shown that the broadening of the impurity level leads to an additional and important contribution to the Fano resonance around the Fermi surface, especially in the mixed valence regime. This contribution results from the interference between the Kondo resonance and the broadened impurity level. Being applied to the scanning tunneling microscopic experiments, we find that our theory gives a consistent and quantitative account for the Fano resonance line shapes for both Co and Ti impurities on Au or Ag surfaces. The Ti systems are found to be in the mixed valence regime.

We have investigated the physical effects of the Dzyaloshinskii-Moriya (DM) interaction in copper benzoate. In the low-field limit, the spin gap is found to vary as H(2/3)ln((1/6)(J/mu(B)H(s)) (H(s): an effective staggered field induced by the external field H) in agreement with the prediction of conformal field theory, while the staggered magnetization varies as H(1/3) and the ln((1/3)(J/mu(B)H(s)) correction predicted by conformal field theory is not confirmed. The linear scaling relation between the momentum shift and the magnetization is broken. We have determined the coupling constant of the DM interaction and have given a complete quantitative account for the field dependence of the spin gaps along all three principal axes, without resorting to additional interactions such as interchain coupling. A crossover to strong applied field behavior is predicted for further experimental verification.

The metal-insulator crossover of the in-plane resistivity upon temperature decrease, recently observed in several classes of cuprate superconductors, when a strong magnetic field suppresses the superconductivity, is explained using the U(1)xSU(2) Chern-Simons gauge field theory. The origin of this crossover is the same as that for a similar phenomenon observed in heavily underdoped cuprates without magnetic field. It is due to the interplay between the diffusive motion of the charge carriers and the "peculiar" localization effect due to short-range antiferromagnetic order. We also calculate the in-plane transverse magnetoresistance which is in fairly good agreement with available experimental data.