Electron-phonon coupling in the undoped cuprate YBa2Cu3O6 estimated from Raman and optical conductivity spectra

We study experimentally the Raman response of the undoped high-${T}_{c}$ parent compound ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6}$, and give a unified theory of the two-magnon Raman peak and optical conductivity based on the Hubbard-Holstein model with electron-phonon coupling (EPC). The Hubbard model without EPC can qualitatively account for the experimentally observed resonance of the Raman response, but only the Hubbard-Holstein model (i) reproduces the asymmetry of the Raman spectrum, (ii) validates the experimental visibility of the two-magnon peak, and (iii) predicts the correct shape and energy of the lower edge of the charge transfer gap in optical conductivity. A comparison of experiments with the theory gives the EPC strength $\ensuremath{\lambda}=0.6$. This result convincingly indicates the vital role of EPC in high-${T}_{c}$ cuprates, providing a clue to the mechanism of high ${T}_{c}$.