Effects of $\tau_1$ Scattering on Fourier-Transformed Inelastic Tunneling Spectra in High-$T_c$ Cuprates with Bosonic Modes

TL;DR

This study investigates how $ au_1$ impurities influence the Fourier-transformed inelastic tunneling spectra in high-$T_c$ cuprates, highlighting the role of electron-boson interactions, especially with the $B_{1g}$ phonon mode, in gap inhomogeneity.

Contribution

It introduces a model linking $ au_1$ impurity effects to bosonic mode coupling, explaining observed spectral patterns in high-$T_c$ cuprates with implications for understanding gap inhomogeneity.

Findings

Pattern similarity with FT-IETS STM experiments in BSCCO.

Anisotropic electron-$B_{1g}$ phonon coupling reproduces experimental features.

Implications for band renormalization effects in ARPES data.

Abstract

We study the $\tau_1$-impurity induced $\mathbf{q}$-space pattern of the energy derivative local density of states (LDOS) in a d-wave superconductor. We are motivated in part by the recent scanning tunneling microscopy (STM) observation of strong gap inhomogeneity with weak charge density variation in Bi$_{2}$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO). The hypothesis is that the gap inhomogeneity might be triggered by the disorder in pair potential. We focus on the effects of electron coupling to various bosonic modes, at the mode energy shifted by the d-wave superconducting gap. The pattern due to a highly anisotropic coupling of electrons to the $B_{1g}$ phonon mode is similar to preliminary results from the Fourier transformed inelastic electron tunneling spectroscopy (FT-IETS) STM experiment in BSCCO. We discuss the implications of our results in the context of band renormalization effects seen in the ARPES experiments, and suggest means to further explore the electron-boson coupling in the high-$T_c$ cuprates.