Fourier transform spectroscopy of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi></mml:math>-wave quasiparticles in the presence of atomic scale pairing disorder

Abstract

The local density of states power spectrum of optimally doped ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}\mathrm{Ca}{\mathrm{Cu}}_{2}{\mathrm{O}}_{8+x}$ (BSCCO) has been interpreted in terms of quasiparticle interference peaks corresponding to an ``octet'' of scattering wave vectors connecting $\mathbf{k}$ points where the density of states is maximal. Until now, theoretical treatments have not been able to reproduce the experimentally observed weights and widths of these octet peaks; in particular, the predominance of the dispersing ``${\mathbf{q}}_{1}$'' peak parallel to the Cu-O bond directions has remained a mystery. In addition, such theories predict ``background'' features which are not observed experimentally. Here, we show that most of the discrepancies can be resolved when a realistic model for the out-of-plane disorder in BSCCO is used. Weak extended potential scatterers, which are assumed to represent cation disorder, suppress large-momentum features and broaden the low-energy ``${\mathbf{q}}_{7}$'' peaks, whereas scattering at order parameter variations, possibly caused by a dopant-modulated pair interaction around interstitial oxygens, strongly enhances the dispersing ${\mathbf{q}}_{1}$ peaks.