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 A₁ 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 A₁ vibrational modes, the quasiequilibrium nuclear A₁ coordinates are displaced with no change in lattice symmetry, giving rise to a coherent vibration of A₁ symmetry about the displaced quasiequilibrium coordinates. One important prediction of the DECP mechanism is the excitation of only modes with A₁ symmetry. Furthermore, the oscillations in the reflectivity R are excited with a cos(ω₀t) dependence, where t=0 is the time of arrival of the pump pulse peak, and ω₀ is the vibrational frequency of the A₁ mode. These predictions agree well with our observations in Bi, Sb, Te, and Ti₂{O}₃$. The fit of the experimental {Δ}R(t)/R(0) data to the theory is excellent.