Superconducting Transition Temperature of the Hole-Doped Cuprate as the Stabilization Temperature of Supercurrent Loops Generated by Spin-Twisting Itinerant Motion of Electrons

A theoretical calculation for the superconducting transition temperature of the hole-doped cuprate is performed based on supercurrent generation by the spin-twisting itinerant motion of electrons. The superconducting transition temperature, T c , is determined by a numerical simulation as the stabilization temperature of the coherence-length-sized loop currents, “spin-vortex-induced loop currents (SVILCs),” generated by the spin-twisting itinerant motion of electrons. The simulation indicates that the stabilization of the SVILCs occurs in two steps; when temperature is decreased from room temperature, first, the phase where the sum of the winding numbers of the SVILCs is zero appears; with further decrease of the temperature, the phase where the winding numbers of the SVILCs are fixed appears. We identify the latter to the superconducting phase, and the former to the temperature below which the Kerr rotation is observed. The calculated T c value is close to the experimental value around the optimal doping. It scales as \({{t^{2}} \over U}\) in a similar manner to the antiferromagnetic spin-fluctuation, where t is the nearest neighbor transfer integral and U is the on-site Coulomb repulsion parameter. The calculated T c disagrees in the underdoped and overdoped regions. These disagreements are explained as due to the reduction of T c by the quantum criticality arising from the two quantum critical points at the lowest and highest ends of the hole density x of the superconducting phase, where the former corresponds to the percolation threshold of the spin-vortices, and the latter to the spin-vortex formation-destruction critical point.