Theory for displacive excitation of coherent phonons

We report femtosecond time-resolved pump-probe reflection experiments in semimetals and semiconductors that show large-amplitude oscillations with periods characteristic of lattice vibrations. Only ${\mathit{A}}_{1}$ modes are detected, although modes with other symmetries are observed with comparable intensity in Raman scattering. We present a theory of the excitation process in this class of materials, which we refer to as displacive excitation of coherent phonons (DECP). In DECP, after excitation by a pump pulse, the electronically excited system rapidly comes to quasiequilibrium in a time short compared to nuclear response times. In materials with ${\mathit{A}}_{1}$ vibrational modes, the quasiequilibrium nuclear ${\mathit{A}}_{1}$ coordinates are displaced with no change in lattice symmetry, giving rise to a coherent vibration of ${\mathit{A}}_{1}$ symmetry about the displaced quasiequilibrium coordinates. One important prediction of the DECP mechanism is the excitation of only modes with ${\mathit{A}}_{1}$ symmetry. Furthermore, the oscillations in the reflectivity R are excited with a cos(${\mathrm{\ensuremath{\omega}}}_{0}$t) dependence, where t=0 is the time of arrival of the pump pulse peak, and ${\mathrm{\ensuremath{\omega}}}_{0}$ is the vibrational frequency of the ${\mathit{A}}_{1}$ mode. These predictions agree well with our observations in Bi, Sb, Te, and ${\mathrm{Ti}}_{2}$${\mathrm{O}}_{3}$. The fit of the experimental \ensuremath{\Delta}R(t)/R(0) data to the theory is excellent.