Kondo Effect in High-TcCuprates

We study the Kondo effect due to the nonmagnetic impurity, e.g., Zn, in high- $T_c$ cuprates based on the spin-change separated state. In the optimal or overdoped case with the Kondo screening, the resistivity is given by $\rho \left(T\right)=\frac{4ħ}{e^2}\frac{n_{\mathrm{imp}}}{1-x}+\frac{\alpha T}{x}$ ( $x$: hole concentration, $n_{\mathrm{imp}}$: impurity concentration, $\alpha$: constant), which is in agreement with experiments. In the underdoped region with the pseudospin gap, an SU(2) formulation predicts that the holon phase shift is related to the formation of the local spin moment, and hence the residual resistivity is given by ${\rho }_{\mathrm{res}}=\frac{4ħ}{e^2}\frac{n_{\mathrm{imp}}}{x}$, which is also consistent with the experiments. The magnetic impurity case, e.g., Ni, is also discussed.