Abstract:
Molecular solids are generally highly insulating. The creation of conducting molecular solids proved to be a major scientific challenge. As in the case of Si technology, the challenge started as impurity doping in band insulators and then developed into highly doped polymers, which are not crystalline. More conducting materials in crystalline forms have been realized in charge transfer (CT) complexes with two different kinds of molecules, where electrons are transferred between them in solids. In such CT complexes, not only conducting, but also even superconducting systems were achieved in 1980 and today more than 100 different superconductors are known. The most remarkable achievement in this direction was the realization of a truly metallic state in molecular solids based on a single kind of molecule. These are called single component molecular metals (SCMM) and consist of a rich variety of electronic properties. In these conducting molecular solids, CT and SCMM, many interesting electronic properties resulting from mutual Coulomb interactions and electron-phonon interactions have been explored so far, and these will be reviewed briefly in this article from a theoretical viewpoint. Challenges to come, based on these achievements, are also discussed at the end of this review.

Abstract:
Various aspects of close and interesting relationship between antiferromagnetism and singlet ground states are introduced for which neutron scattering have been playing vital roles. The special emphasis is on the disorder-induced antiferromagnetism in spin-Peierls systems, which can be viewed as a nucleation process of classical magnetic order in the background of singlet state whose origin is purely quantum-mechanical. It is then pointed out that similar features will be found in Ce_xCu_2Si_2 and high T_c cuprates. Finally the possible charge ordering process in NaV_2O_5 is discussed which leads to the quenching of localized spins.

Abstract:
It is shown that the energy $(\varepsilon)$ and momentum $(k)$ dependences of the electron self-energy function $ \Sigma (k, \varepsilon + i0) \equiv \Sigma^{R}(k, \varepsilon) $ are, $ {\rm Im} \Sigma^{R} (k, \varepsilon) = -a\varepsilon^{2}|\varepsilon - \xi_{k}|^{- \gamma (k)} $ where $a$ is some constant, $\xi_{k} = \varepsilon(k)-\mu, \varepsilon(k)$ being the band energy, and the critical exponent $ \gamma(k) $, which depends on the curvature of the Fermi surface at $ k $, satisfies, $ 0 \leq \gamma(k) \leq 1 $. This leads to a new type of electron liquid, which is the Fermi liquid in the limit of $ \varepsilon, \xi_{k} \rightarrow 0 $ but for $ \xi_{k} \neq 0 $ has a split one-particle spectra as in the Tomonaga-Luttinger liquid.

Abstract:
A new method has been proposed to evaluate the frictional force in the stationary state. This method is applied to the 1-dimensional model of clean surfaces. The kinetic frictional force is seen to depend on velocity in general, but the dependence becomes weaker as the maximum static frictional force increases and in the limiting case the kinetic friction gets only weakly dependent on velocity as described by one of the laws of friction. It is also shown that there is a phase transition between state with vanishing maximum static frictional force and that with finite one. The role of randomness at the interface and the relation to the impurity pinning of the sliding Charge-Density-Wave are discussed. to appear in Phys.Rev.B. abstract only. Full text is available upon request. E-mail: hiro@ena.wani.osaka-u.ac.jp.

Abstract:
The doped Mott insulator in one dimension has been studied based on the phase Hamiltonian with the Umklapp scattering process, in which the charge degree of freedom is described by the quantum sine-Gordon model. The well-known equivalence between the quantum sine-Gordon model and the massive Thirring model for the spinless fermion makes it clear that the Mott-Hubbard gap originates from the Umklapp scattering process as was indicated by Emery and Giamarchi. Compressibility, density-density correlation function, frequency dependence of optical conductivity and Drude weight have been calculated in the presence of the impurity scattering treated in the self-consistent Born approximation. It is seen that there exists a crossover behavior in the spectral weight of charge excitations: the acoustic mode is dominant in small wave number region while the optical excitations across the Mott-Hubbard gap lie in large wave number region and that this crossover wave number is reduced as the Mott transition is approached.

Abstract:
The resistivity due to a domain wall in ferromagnetic metallic wire is calculated based on the linear response theory. The interaction between conduction electrons and the wall is expressed in terms of a classical gauge field which is introduced by the local gauge transformation in the electron spin space. It is shown that the wall contributes to the decoherence of electrons and that this quantum correction can dominate over the Boltzmann resisitivity, leading to a decrease of resisitivity by nucleation of a wall. The conductance fluctuation due to the motion of the wall is also investigated. The results are compared with recent experiments.

Abstract:
The macroscopic quantum tunneling of a planar domain wall in a ferromagnetic metal is studied based on the Hubbard model. It is found that the ohmic dissipation is present even at zero temperature due to the gapless Stoner excitation, which is the crucial difference from the case of the insulating magnet. The dissipative effect is calculated as a function of width of the wall and is shown to be effective in a thin wall and in a weak ferromagnet. The results are discussed in the light of recent experiments on ferromagnets with strong anisotropy. PACS numbers:75.60.Ch, 03.65.Sq, 75.10.Lp

Abstract:
The depinning of a domain wall in ferromagentic metal via macroscopic quantum tunneling is studied based on the Hubbard model. The dynamics of the magnetization verctor is shown to be governed by an effective action of Heisenberg model with a term non-local in time that describes the dissipation due to the conduction electron. Due to the existence of the Fermi surface there exists Ohmic dissipation even at zero temperature, which is crucially different from the case of the insulator. Taking into account the effect of pinning and the external magnetic field the action is rewritten in terms of a collective coordinate, the position of the wall, $Q$. The tunneling rate for $Q$ is calculated by use of the instanton method. It is found that the reduction of the tunneling rate due to the dissipation is very large for a thin domain wall with thickness of a few times the lattice spacing, but is negligible for a thick domain wall. Dissipation due to eddy current is shown to be negligible for a wall of mesoscopic size.

Abstract:
The macroscopic quantum tunneling of a planar domain wall in a ferromagnetic metal is studied by use of an instanton method. Based on the Hubbard model, the effective action of the magnetization is derived within the assumption of slow dependences on space and time. The resulting action is formally similar to that of a ferromagnetic Heisenberg model but with a term non-local in time that describes the dissipation due to the itinerant electron. The crucial difference from the case of the insulator is the presence of the ohmic dissipation even at zero temperature due to the gapless Stoner excitation. The reduction of the tunneling rate due to the dissipation is calculated. The dissipative effect is found to be very large for a thin domain wall with thickness of a few times the lattice spacing, but is negligible for a thick domain wall. The results are discussed in the light of recent experiments on ferromagnets with strong anisotropy. (Submitted to J. Phys. Soc. Jpn)

Abstract:
The real part of the self-energy of interacting two-dimensional electrons has been calculated in the t-matrix approximation. It is shown that the forward scattering results in an anomalous term leading to the vanishing renormalization factor of the one-particle Green function, which is a non-perturbative effect of the interaction U. The present result is a microscopic demonstration of the claim by Anderson based on the conventional many-body theory. The effect of the damping of the interacting electrons, which has been ignored in reaching above conclusion, has been briefly discussed.