Quantum Interference of Impurity Bound States in Bi$_{2}$Sr$_{2}$Ca(Cu$_{1-x}$Zn$_{x}$)$_{2}$O$_{8+\delta}$ Probed by Scanning Tunneling Spectroscopy

TL;DR

This study uses scanning tunneling microscopy to explore how non-magnetic impurities interact in a high-temperature d-wave superconductor, revealing quantum interference effects that influence impurity band formation.

Contribution

It provides direct experimental evidence of quantum interference of impurity bound states in a high-Tc superconductor using STM, highlighting spatial modulations and energy variations.

Findings

Observation of 5.4 Å density-of-states modulation indicating d-wave symmetry

Detection of abrupt changes in impurity bound state energies

Identification of positive energy states and split impurity states

Abstract

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 expected 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.