Role of non-magnetic disorder in a doped U(1) spin liquid

Recently we investigated a role of non-magnetic disorder on the stability of a U(1) spin liquid ($U1SL$) [cond-mat/0407151; Phys. Rev. B (R) accepted]. In the present paper we examine an effect of the non-magnetic disorder on a doped $U1SL$. In a recent study [cond-mat/0408236] we have shown that the doped $U1SL$ shows deconfined massive spinon excitations in the superconducting phase as a result of holon condensation. We find that the massive spinon is trapped by the non-magnetic disorder. Owing to the localized spin the non-magnetic disorder acts as magnetic one.