On the relative positions of the $2\Delta$ peaks in Raman and tunneling spectra of d-wave superconductors

TL;DR

This paper investigates the relationship between Raman and tunneling spectra peaks in d-wave superconductors, analyzing how impurity-induced damping influences peak positions and their experimental implications.

Contribution

It provides a detailed analysis of how fermionic damping affects peak positions in Raman and tunneling spectra in d-wave superconductors, clarifying their relative shifts.

Findings

Peak in Raman spectra remains near twice the tunneling peak despite damping.

Damping shifts peaks to higher frequencies but does not explain the observed downturn shift.

The study discusses damping effects on dynamical spin susceptibility.

Abstract

We study $B_{1g}$ Raman intensity $R(\Omega)$ and the density of states $N(\omega)$ in isotropic 2D d-wave superconductors. For an ideal gas, $R(\Omega)$ and $N(\omega)$ have sharp peaks at $\Omega =2\Delta$ and $\omega =\Delta$, respectively, where $\Delta$ is the maximum value of the gap. We study how the peak positions are affected by the fermionic damping due to impurity scattering. We show that while the damping generally shifts the peak positions to larger frequencies, the peak in $R(\Omega)$ still occurs at almost twice the peak position in $N(\omega)$ and therefore cannot account for the experimentally observed downturn shift of the peak frequency in $R(\Omega)$ in underdoped cuprates compared to twice that in $N(\omega)$. We also discuss how the fermionic damping affects the dynamical spin susceptibility.