Electron-phonon coupling in undoped cuprate $YBa_2Cu_3O_6$ estimated from Raman and optical conductivity spectra

We study experimentally the Raman response of the undoped high-Tc parent compound $YBa_2Cu_3O_6$, 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 asymmetry of the Raman spectrum, (ii) validates 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. Comparison of experiments with the theory gives the EPC strength $\lambda$ = 0.6. This result convincingly indicates the vital role of EPC in high-Tc cuprates providing a clue to the mechanism of high-Tc.