Effect of unitary impurities on non-STM types of tunneling in high-Tcsuperconductors

Abstract

Based on an extended Hubbard model, we present calculations of both the local (i.e., single-site) and spatially averaged differential tunneling conductance in d-wave superconductors containing nonmagnetic impurities in the unitary limit. Our results show that a random distribution of unitary impurities of any concentration can at most give rise to a finite zero-bias conductance (with no peak there) in spatially averaged non-STM type of tunneling. This is in spite of the fact that local tunneling in the immediate vicinity of an isolated impurity does show a conductance peak at zero bias. We also find that to give rise to even a small zero-bias conductance peak in the spatially averaged type of tunneling the impurities must form dimers, trimers, etc., along the [110] directions. In addition, we find that the most recently observed novel pattern of the tunneling conductance around a single impurity by Pan et al. [Nature (London) 403, 746 (2000)] can be explained in terms of a realistic model of the tunneling configuration which gives rise to the experimental results reported there. The key feature in this model is the blocking effect of the BiO and SrO layers which exist between the tunneling tip and the ${\mathrm{CuO}}_{2}$ layer being probed.