Doping dependence of the nonmagnetic impurity resonance in cuprate superconductors

Motivated by the observation that the nonmagnetic impurity induced resonance strength is reduced with underdoping in Bi(2)Sr2Ca(Cu1-yZny)(2)O8+x, we study the doping dependence of the nonmagnetic impurity induced resonance in cuprates from the viewpoint of resonating valence bond (RVB) spin liquid theory. It is revealed that the pseudogap state in the Yang, Rice and Zhang ansatz (Yang et al 2006 Phys. Rev. B 73 174501; Rice et al 2012 Rep. Prog. Phys. 75 016502) does not support an impurity resonance state due to the overdamping of the quasiparticle. In the coexistence of the d-wave superconductivity and the RVB gap, our theory provides an alternative but consistent explanation for the reduction of the resonance strength with underdoping, as well as the absence of the resonance in the large gap region.