  We propose a mechanism of unconventional superconductivity in two-dimensional strongly-correlated electron systems. We consider a two-dimensional Kondo lattice system or double-exchange system with spin-orbit coupling arising from buckling of the plane. We show that a Chern-Simons term is induced for a gauge field describing the phase fluctuations of the localized spins. Through the induced Chern-Simons term, carriers behave like skyrmion excitations that lead to a destruction mechanism of magnetic long-range order by carrier doping. After magnetic long-range order is destroyed by carrier doping, the Chern-Simons term plays a dominant role and the attractive interaction between skyrmions leads to unconventional superconductivity. For the case of the ferromagnetic interaction between the localized spins, the symmetry of the Cooper pair is p-wave ($p_x \pm ip_y$). For the case of the antiferromagnetic interaction between the localized spins, the symmetry of the Cooper pair is d-wave ($d_{x^2-y^2}$). Applications to various systems are discussed, in particular to the high-$T_c$ cuprates. 
Mechanism of unconventional superconductivity induced by skyrmion   excitations in two-dimensional strongly-correlated electron systems