Impurity states in d-wave superconductors with a competing antiferromagnetic interaction

Abstract

Impurity states in d-wave superconductors with a competing antiferromagnetic (AF) order are investigated by solving the Bogoliubov-de Gennes equations. The potential scattering (PS) model with moderate strength and the Anderson impurity (AI) model with on-site hybridization are employed to describe the weak impurities. In zero external field, the impurity-induced AF order is rather weak and both models are able to give rise to impurity resonant states with close energy and similar profile of the local density of states. In the mixed state, the effect of magnetic-field-induced AF order on the impurity quasiparticle excitation is also examined. We find that the response of the impurity state to the presence of a local AF order is quite different for the two impurity models when a superconducting vortex is pinned by the impurity. For the PS model, the impurity resonance is subtly dependent on the sign and strength of the scattering potential, while for the AI model in the strong hybridization regime, the low-lying resonance is pinned near the Fermi level within the small gap opened by the AF order and is insensitive to the strength of the coupling between the impurity spin and the conduction electron. Based on our numerical results, we think that the two models give rise to different behaviors of the impurity resonances for both the nickel and zinc impurities in the magnetic field and the prospective scanning tunneling microscopic observation might give a clue to the dominant mechanism of the impurity states in the high-T c cuprates.