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We study the $\tau_1$-impurity induced $\mathbf{q}$-space pattern of theenergy derivative local density of states (LDOS) in a d-wave superconductor. Weare motivated in part by the recent scanning tunneling microscopy (STM)observation of strong gap inhomogeneity with weak charge density variation inBi$_{2}$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO). The hypothesis is that the gapinhomogeneity might be triggered by the disorder in pair potential. We focus onthe effects of electron coupling to various bosonic modes, at the mode energyshifted by the d-wave superconducting gap. The pattern due to a highlyanisotropic coupling of electrons to the $B_{1g}$ phonon mode is similar topreliminary results from the Fourier transformed inelastic electron tunnelingspectroscopy (FT-IETS) STM experiment in BSCCO. We discuss the implications ofour results in the context of band renormalization effects seen in the ARPESexperiments, and suggest means to further explore the electron-boson couplingin the high-$T_c$ cuprates.Comment: 5 pages, 2 eps figures include

physical review letters

Effects of Pairing Potential Scattering on Fourier-Transformed Inelastic Tunneling Spectra of High-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mi>c</mml:mi></mml:msub></mml:math>Cuprate Superconductors with Bosonic Modes

Effects of Pairing Potential Scattering on Fourier-Transformed Inelastic Tunneling Spectra of High-TcCuprate Superconductors with Bosonic Modes