Charge transfer fluctuation, $d-$wave superconductivity, and the $B_{1g}$ Raman phonon in the Cuprates: A detailed analysis

TL;DR

This paper provides a detailed theoretical analysis of the $B_{1g}$ Raman phonon in cuprate superconductors, linking charge transfer fluctuations to electron-phonon interactions and phonon lineshape changes across the superconducting transition.

Contribution

It introduces a model connecting charge transfer fluctuations to the $B_{1g}$ phonon lineshape, offering insights into the superconducting gap symmetry through Raman spectroscopy.

Findings

Excellent agreement with experimental phonon lineshape in YBa2Cu3O7

Change in linewidth below Tc consistent with d-wave pairing

Analysis distinguishes effects of different pairing symmetries

Abstract

The Raman spectrum of the $B_{1g}$ phonon in the superconducting cuprate materials is investigated theoretically in detail in both the normal and superconducting phases, and is contrasted with that of the $A_{1g}$ phonon. A mechanism involving the charge transfer fluctuation between the two oxygen ions in the CuO$_2$ plane coupled to the crystal field perpendicular to the plane is discussed and the resulting electron-phonon coupling is evaluated. Depending on the symmetry of the phonon the weight of different parts of the Fermi surface in the coupling is different. This provides the opportunity to obtain information on the superconducting gap function at certain parts of the Fermi surface. The lineshape of the phonon is then analyzed in detail both in the normal and superconducting states. The Fano lineshape is calculated in the normal state and the change of the linewidth with temperature below T$_{c}$ is investigated for a $d_{x^{2}-y^{2}}$ pairing symmetry. Excellent agreement is obtained for the $B_{1g}$ phonon lineshape in YBa$_{2}$Cu$_{3}$O$_{7}$. These experiments, however, can not distinguish between $d_{x^{2}-y^{2}}$ and a highly anisotropic $s$-wave pairing.