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abstract: 'Impurity resonances observed by scanning tunneling spectroscopy in the superconducting state have been used to deduce properties of the underlying pure state. Here we study a longstanding puzzle associated with these measurements, the apparent extinction of these resonances for Ni and Zn impurities in large-gap regions of the inhomogeneous [[Bi$_2$Sr$_2$CaCu$_2$O$_{8+x}$ ]{}]{}superconductor. We calculate the effect of order parameter and hopping suppression near the impurity site, and find that these two effects are sufficient to explain the missing resonances in the case of Ni. There are several possible scenarios for the extinction of the Zn resonances, which we discuss in turn; in addition, we propose measurements which could distinguish among them.'
author:
- 'Brian M. Andersen$^1$, S. Graser$^2$, and P. J. Hirschfeld$^2$'
title: 'Extinction of impurity resonances in large-gap regions of inhomogeneous $d$-wave superconductors'
---

Introduction
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An understanding of the low doped Mott region of cuprate superconductors remains a key problem in condensed matter physics.[@leereview] It has been proposed that electronic inhomogeneity is crucial for explaining experiments performed in the underdoped regime,[@sakivelson] and that the inhomogeneity arises from strong Coulomb repulsion which instigates the formation of spin- and charge density waves, enhanced and pinned by a random potential 