Antiferromagnetic spin fluctuation and superconductivity

In this review, we summarize the present status of theories of the spin fluctuation (SF) mechanism in explaining anomalous or non-Fermi liquid behaviours and unconventional superconductivity (SC) in strongly correlated electron systems around the antiferromagnetic (AF) quantum critical point. We refer to the high-T_c cuprates, two-dimensional organic compounds and heavy electron systems. We argue that the SF theories are successful in explaining at least the essential part of the problems, indicating that AF SF is the common origin of SC in these systems. This review is concluded by several comments on remaining problems which may require some additions to the SF theory, like the pseudo-gap phenomena observed in the hole-underdoped cuprates.