Symmetry dependence of phonon lineshapes in superconductors with anisotropic gaps

TL;DR

This paper investigates how the symmetry of electron-phonon interactions affects phonon lineshapes in superconductors with anisotropic gaps, explaining experimental observations in Raman scattering.

Contribution

It provides a detailed theoretical analysis of phonon lineshape changes due to anisotropic gaps, focusing on $B_{1g}$ and $A_{1g}$ phonons in $d_{x^{2}-y^{2}}$ superconductors.

Findings

Substantial narrowing of $B_{1g}$ phonon lineshape observed.

$A_{1g}$ phonon lineshape remains similar to the normal state.

Theory agrees with recent Raman measurements on BSCCO.

Abstract

The temperature dependence below $T_{c}$ of the lineshape of optical phonons of different symmetry as seen in Raman scattering is investigated for superconductors with anisotropic energy gaps. It is shown that the symmetry of the electron-phonon vertex produces non-trivial couplings to an anisotropic energy gap which leads to unique changes in the phonon lineshape for phonons of different symmetry. The phonon lineshape is calculated in detail for $B_{1g}$ and $A_{1g}$ phonons in a superconductor with $d_{x^{2}-y^{2}}$ pairing symmetry. The role of satellite peaks generated by the electron-phonon coupling are also addressed. The theory accounts for the substantial phonon narrowing of the $B_{1g}$ phonon, while narrowing of the $A_{1g}$ phonon which is indistinguishable from the normal state is shown, in agreement with recent measurements on BSCCO.