A planar Mott insulator with easy plane N\'eel order can be mapped onto a Gutzwiller-projected spin Hall state. The in-plane substitution of Zn$^{ 2+}$ and Li$^{ +}$ for Cu$^{ 2+}$ brings zero modes around the spin vacancy. The Gutzwiller projection precludes single particle excitations, however, preserves the zero modes which have a local spin moment for Zn$^{ 2+}$ and a local charged hole for Li$^{ +}$, respectively. While the local spin moment for Zn$^{ 2+}$ is screened by the long-range spin correlations, the active charge degree of freedom for Li$^{ +}$ impurity twists the spin background with long ranged disturbances. This proposal explains the very different roles of the Zn$^{ 2+}$ and Li$^{ +}$ impurities on the magnetic perturbations in the CuO$_2$ plane in the undoped cuprate compounds.
Categories: cond-mat.str-el