Abstract
When spin vortices are present, loop currents arise around them. These loop currents are germs of a macroscopic current, i.e., a macroscopic current is created as a collection of them, and eventually form a persistent current at temperatures below Tc. We argue that this is what happening in the underdoped cuprates. The hourglass-shaped magnetic excitation spectrum observed in cuprates is considered as evidence of the presence of spin vortices; the Drude-like peak in the optical conductivity is also explained as arising from spin-wave excitations in the presence of spin vortices. The observed enhanced Nernst signals and magnetization in the psudogap phase is explained due to the flow of the loop currents. If we calculate Tc in the underdoped sample as the temperature where the coherence establishes among the loop currents, the doping concentration dependence of it is given by Tc=T0lnxx0, which is shown to agree well with experiments.
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