Topological Aspects of High Temperature Superconductivity and Berry Phase

We propose a mechanism of high temperature superconductivity from the viewpoint of chirality and Berry phase. It is observed that spin pairing and charge pairing is caused by a gauge force generated by magnetic flux quanta attached to them. From the renormalization group equation involving the Berry phase factor $\mu$ it is found that there are two crossovers above the superconducting temperature $T_c$, one corresponds to the glass phase and the other represents the spin gap phase. Actually, in this topological framework each charge carrier is dressed with a magnetic flux quantum and represents a skyrmion. The skyrmion-skyrmion bound state leads to the d-wave Cooper pair formation. We have also discussed the Magnus force acting on the vortices of this system.