In this article we review essential natures of superconductivity in strongly correlated electron systems (SCES) from a universal point of view. First we summarize experimental results on SCES by focusing on typical materials such as cuprates, BEDT-TTF organic superconductors, and ruthenate Sr 2 RuO 4 . Experimental results on other important SCES, heavy-fermion systems, will be reviewed separately. The formalism to discuss superconducting properties of SCES is shown based on the Dyson-Gor'kov equations. Here two typical methods to evaluate the vertex function are introduced: One is the perturbation calculation up to the third-order terms with respect to electron correlation. Another is the fluctuationexchange (FLEX) method based on the Baym-Kadanoff conserving approximation. The results obtained by the FLEX method are in good agreement with those obtained by the perturbation calculation. In fact, a reasonable value of T c for spin-singlet d-wave superconductivity is successfully reproduced by using both methods for SCES such as cuprates and BEDT-TTF organic superconductors. As for Sr 2 RuO 4 exhibiting spin-triplet superconductivity, it is quite difficult to describe the superconducting transition by using the FLEX calculation. However, the superconductivity can be naturally explained by the perturbation calculation, since the third-order terms in the anomalous self-energy play the essential role to realize the triplet superconductivity. Another important purpose of this article is to review anomalous electronic properties of SCES near the Mott transition, since the nature of the normal state in SCES has been one of main issues to be discussed. Especially, we focus on pseudogap phenomena observed in under-doped cuprates and organic superconductors. A variety of scenarios to explain the pseudogap phenomena based on the superconducting and/or spin fluctuations are critically reviewed and examined in comparison with experimental results. According to the recent theory, superconducting fluctuations, inherent in the quasi-two-dimensional and strong-coupling superconductors, are the origin of the pseudogap formation. In these compounds, superconducting fluctuations induce a kind of resonance between the Fermi-liquid quasi-particle and the Cooper-pairing states. This resonance gives rise to a large damping effect of quasi-particles and reduces the spectral weight near the Fermi energy. We discuss the magnetic and transport properties as well as the single-particle spectra in the pseudogap state by the microscopic theory of the superconducting fluctuations. As for heavy-fermion superconductors, experimental results are reviewed and several theoretical analyses on the mechanism are provided based on the same viewpoint as explained above.

To investigate a mysterious superconducting state of URu2Si2 embedded in the so-called hidden order state, the lower critical field Hc1 is precisely determined down to 55 mK for H a and H c. For this purpose, the positional dependence of the local magnetic induction is measured on ultraclean single crystals (Tc = 1.4 K) with residual resistivity ratio exceeding 700. We find that the temperature dependence of Hc1 significantly differs from that of any other superconductors. The whole Hc1(T ) for H a are well explained by the two superconducting gap structures with line and point nodes, which have been suggested by the recent thermal conductivity and specific heat measurements. On the other hand, for H c, a change of slope with a distinct kink in Hc1(T ), which cannot be accounted for by two gaps, is observed. This behavior for H c sharply contrasts with the cusp behavior of Hc1(T ) associated with a transition into another superconducting phase found in UPt3 and U1−xThxBe13. The observed anomalous low-field diamagnetic response is possibly related to a peculiar vortex dynamics associated with chiral domains due to the multicomponent superconducting order parameter with broken time reversal symmetry.

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