Displacive excitation of coherent phonons in ${\mathrm{YBa}}_2$${\mathrm{Cu}}_3$${\mathrm{O}}_7$

We suggest a microscopic model that provides a consistent explanation of the recent femtosecond pump-probe experiments on ${\mathrm{YBa}}_2$ ${\mathrm{Cu}}_3$ ${\mathrm{O}}_7$, including the fact that the reflectivity change in the superconducting state is much larger than that in the normal state. In this model, not only the oscillatory part of the reflectivity, but also the total reflectivity change, is due to displacive excitation of coherent phonons. The microscopic reason for this excitation is that superconductivity induces small displacements in the equilibrium positions of the ions, since the pairing energy depends on the density of states at the Fermi level, which changes with the ionic positions. When superconductivity is destroyed by the femtosecond laser pulse, the ions are pulled back to their normal equilibrium positions, thus exciting coherent phonons. The relative size of the oscillatory contribution to the reflectivity depends upon the ratio of the phonon period to the time scale of the pair breaking, and when this ratio is small, the oscillations are suppressed, as observed in the experiment. Ab initio caluclations confirm this model. The model also provides an explanation for why the mangitude of the 150 ${\mathrm{cm}}^{\mathrm{-}1}$ mode below ${\mathit{T}}_{\mathit{c}}$ may be smaller than that of the 120 ${\mathrm{cm}}^{\mathrm{-}1}$ mode.