In conventional superconductors, magnetic impurities form an impurity band due to quantum interference of the impurity bound states, leading to suppression of the superconducting transition temperature. Such quantum interference effects can also be e
xpected in d-wave superconductors. Here, we use scanning tunneling microscopy to investigate the effect of multiple non-magnetic impurities on the local electronic structure of the high-temperature superconductor Bi$_{2}$Sr$_{2}$Ca(Cu$_{1-x}$Zn$_{x}$)$_{2}$O$_{8+delta}$. We find several fingerprints of quantum interference of the impurity bound states including: (i) a two-dimensional modulation of local density-of-states with a period of approximately 5.4 AA along the $a$- and $b$-axes, which is indicative of the d-wave superconducting nature of the cuprates; (ii) abrupt spatial variations of the impurity bound state energy; (iii)an appearance of positive energy states; (iv) a split of the impurity bound state. All of these findings provide important insight into how the impurity band in d-wave superconductors is formed.
Using Scanning tunneling spectroscopy (STS), we report the correlation between spatial gap inhomogeneity and the zinc (Zn) impurity resonance in single crystals of Bi$_{mathrm{2}}$Sr$_{mathrm{2}}$Ca(Cu$_{mathrm{1-}x}$Zn$_{x}$)$_{mathrm{2}}$O$_{mathrm
{8+}delta}$ with different carrier (hole) concentrations ($p$) at a fixed Zn concentration ($x$ $sim$ 0.5 % per Cu atom). In all the samples, the impurity resonance lies only in the region where the gap value is less than $sim$ 60 meV. Also the number of Zn resonance sites drastically decreases with decreasing $p$, in spite of the fixed $x$. These experimental results lead us to a conclusion that the Zn impurity resonance does not appear in the large gap region although the Zn impurity evidently resides in this region.
