Abstract:
We present a theoretical study on the superconductivity in \beta'-(BEDT-TTF)_2ICl_2 at Tc=14.2K under high hydrostatic pressure found by Taniguchi et al., which is the highest record among organic superconductors. Its electronic structure is well expressed by the anisotropic triangular lattice Hubbard model at half filling. In the present work, we study this effective model by using the fluctuation-exchange (FLEX) approximation. In the obtained phase diagram, the superconductivity with d_{x^2-y^2} like symmetry is realized next to the antiferromagnetic (AF) insulating phase, as a result of the 1D-2D dimensional crossover driven by the pressure. The obtained maximum Tc is 16-18K. In addition, the superconductivity in \beta-(BEDT-TTF)_2X is also understood in the same framework.

Abstract:
We present a theoretical study of the Kadowaki-Woods relation in the orbitally degenerate periodic Anderson model. Based on Fermi liquid theory, we derive the generalized Kadowaki-Woods relation in the strong coupling limit, $A\gamma^{-2} \approx 10^{-5} N(N-1)/2$ [\mu\Omega cm(mol K/mJ)^2], where $A$ is the coefficient of the $T^2$ term in the resistivity, $\gamma$ is the $T$-linear specific heat coefficient, and $N$ is the $f$-orbital degeneracy. This result naturally explains the remarkably smaller value of $A\gamma^{-2}$ in various orbitally degenerate (mainly Yb-based) heavy Fermion systems, reported by Tsujii et al.: J. Phys. Cond. Mat. 15 (2003) 1993.

Abstract:
We study AC conductivities in high-Tc cuprates, which offer us significant information to reveal the true electronic ground states. Based on the fluctuation-exchange (FLEX) approximation, current vertex corrections (CVC's) are correctly taken into account to satisfy the conservation laws. We find the significant role of the CVC's on the optical Hall conductivity in the presence of strong antiferromagnetic (AF) fluctuations. This fact leads to the failure of the relaxation time approximation (RTA). As a result, experimental highly unusual behaviors, (i) prominent frequency and temperature dependences of the optical Hall coefficient, and (ii) simple Drude form of the optical Hall andge for wide range of frequencies, are satisfactorily reproduced. In conclusion, both DC and AC transport phenomena in (slightly under-doped) high-Tc cuprates can be explained comprehensively in terms of nearly AF Fermi liquid, if one take the CVC's into account.

Abstract:
Famous non-Fermi liquid-like behaviors of the transport phenomena in high-Tc cuprates (Hall coefficient, magnetoresistance, thermoelectric power, Nernst coefficient, etc) are caused by the current vertex corrections in neary antiferromagnetic (AF) Fermi liquid, which was called the backflow by Landau. We present a simple explaination why the backflow is prominent in strongly correlated systems. In nearly AF Fermi liquid, R_H is enhanced by the backflow because it changes the effective curvature of the Fermi surfaces. Therefore, the relaxation time approximation is not appricalbe to a system near a magnetic quantum critical point (QCP).

Abstract:
In many strongly correlated electron systems, remarkable violation of the relaxation time approximation (RTA) is observed. The most famous example would be high-Tc superconductors (HTSCs), and similar anomalous transport phenomena have been observed in metals near their antiferromagnetic (AF) quantum critical point (QCP). Here, we develop a transport theory involving resistivity and Hall coefficient on the basis of the microscopic Fermi liquid theory, by considering the current vertex correction (CVC). In nearly AF Fermi liquids, the CVC accounts for the significant enhancements in the Hall coefficient, magnetoresistance, thermoelectric power, and Nernst coefficient in nearly AF metals. According to the numerical study, aspects of anomalous transport phenomena in HTSC are explained in a unified way by considering the CVC, without introducing any fitting parameters; this strongly supports the idea that HTSCs are Fermi liquids with strong AF fluctuations. In addition, the striking \omega-dependence of the AC Hall coefficient and the remarkable effects of impurities on the transport coefficients in HTSCs appear to fit naturally into the present theory. The present theory also explains very similar anomalous transport phenomena occurring in CeCoIn5 and CeRhIn5, which is a heavy-fermion system near the AF QCP, and in the organic superconductor \kappa-(BEDT-TTF).

Abstract:
On the basis of the linear response transport theory, the general expressions for the thermoelectric transport coefficients, such as thermoelectric power (S), Nernst coefficient (\nu), and thermal conductivity (\kappa), are derived by using the Fermi liquid theory. The obtained expression is exact as for the most singular term in terms of 1/\gamma_k^* (\gamma_k^* being the quasiparticle damping rate). We utilize the Ward identities for the heat current which is derived by the local energy conservation law. Based on the derived expressions, we can calculate various thermoelectric transport coefficients within the framework of the Baym-Kadanoff type conserving approximation. Thus, the present expressions are very useful for studying the strongly correlated electrons such as high-Tc superconductors, organic metals, and heavy Fermion systems, where the current vertex corrections are expected to play important roles. By using the derived expression, we calculate the thermal conductivity \kappa in a free-dispersion model up to the second-order with respect to U. We find that it is slightly enhanced due to the vertex correction for the heat current, although the vertex correction for electron current makes the conductivity (\sigma) of this system diverge, reflecting the absence of the Umklapp process.

Abstract:
In hole-doped high-Tc cuprates, the Nernst coefficient (\nu) as well as the magnetoresistance (\Delta\rho/\rho) increase drastically below the pseudo-gap temperature, T^*. This unexpected result attracts much attention in that it reflects the fundamental feature of the electronic state in the pseudo-gap region, which has been a central issue on high-Tc cuprates. In this letter, we study these transport phenomena in terms of the fluctuation-exchange (FLEX)+T-matrix approximation. In this present theory, the d-wave superconducting (SC) fluctuations, which are mediated by antiferromagnetic (AF) correlations, become dominant below T^*. We focus on the role of the vertex corrections both for the charge current and the heat one, which are indispensable to keep the conservation laws. As a result, the mysterious behaviors of \nu and \Delta\rho/\rho, which are the key phenomena in the pseudo-gap region, are naturally explained as the reflection of the enhancement of the SC fluctuation, without assuming thermally excited vortices. The present result suggests that the pseudo-gap region in high-Tc cuprates is well described in terms of the Fermi liquid with AF and SC fluctuations.

Abstract:
In high-Tc cuprates, the orbital magnetoresistance in plane (MR, $\Delta\rho/\rho$) is anomalously enhanced at lower tempemeratures compared with conventional Fermi liquids, and thus Kohler's rule is strongly violated. Moreover, it should be noted that an intimate relation between the MR and the Hall coefficient ($R_H$), $\Delta\rho/\rho \propto (R_H/\rho)^2$, holds well experimentally, and is called the "modified Kohler's rule". In this letter, we study this long-standing problem in terms of the nearly antiferromagnetic (AF) Fermi liquid. We analyze the exact expression for the MR by including the vertex corrections (VC's) to keep the conservation laws, and find the approximate "scaling relation" $\Delta\rho/\rho \propto \xi_{AF}^4 /\rho^2$ ($\xi_{AF}$ being the AF correlation length.) in the presence of AF fluctuations. The factor $\xi_{AF}^4$, which comes from the VC's for the current, gives the additional temperature dependence. By taking account of the relation $R_H \propto \xi_{AF}^2$ [Kontani et al., PRB 59 (1999) 14723.], we can naturally explain the modified Kohler's rule. In conclusion, based on the Fermi liquid theory, the famous {\it seemingly} non-Fermi liquid behaviors of the Hall coefficient and the MR in high-Tc cuprates are naturally understood on an equal footing.

Abstract:
The general expression for the magnetoresistance (MR) due to the Lorentz force is derived by using the Fermi liquid transport theory based on the Kubo formula. The obtained gauge-invariant expression is exact for any strength of the interaction, as for the most singular term with respect to 1/\gamma^\ast (\gammak^\ast being the quasiparticle damping rate). By virtue of the exactness, the conserving laws are satisfied rigorously in the present expression, which is indispensable for avoiding unphysical solutions. Based on the derived expression, we can calculate the MR within the framework of the Baym-Kadanoff type conserving approximation, by including all the vertex corrections required by the Ward identity. The present expression is significant especially for strongly correlated systems because the current vertex corrections will be much important. On the other hand, if we drop all the vertex corrections in the formula, we get the MR of the relaxation time approximation (RTA), which is commonly used because of the simplicity. However, the RTA is dangerous because it may give unphysical results owing to the lack of conserving laws. In conclusion, the present work enables us to study the MR with satisfying the conserving laws which is highly demanded in strongly correlated electrons, such as high-Tc superconductors, organic metals, and heavy Fermion systems. In Appendix D, we reply to the comment by O. Narikiyo [cond-mat/0006028]. (Note that Appendix D exists only in the e-preprint version.)

Abstract:
We present a microscopic theory for the thermoelectric power (TEP) in high-Tc cuprates. Based on the general expression for the TEP, we perform the calculation of the TEP for a square lattice Hubbard model including all the vertex corrections necessary to satisfy the conservation laws. In the present study, characteristic anomalous temperature and doping dependences of the TEP in high-Tc cuprates, which have been a long-standing problem of high-Tc cuprates, are well reproduced for both hole- and electron-doped systems, except for the heavily under-doped case. According to the present analysis, the strong momentum and energy dependences of the self-energy due to the strong antiferromagnetic fluctuations play an essential role in reproducing experimental anomalies of the TEP.