Phonon dispersion relations and softening in photoexcited bismuth from first principles

The phonon dispersion relations for equilibrium and photoexcited bismuth are calculated from first-principles density-functional perturbation theory, with constrained occupation of excited electronic states. The dependence of phonon frequency on photoexcited electron-hole plasma density is found for modes throughout the Brillouin zone. The resulting phonon dispersion curves are in good agreement with available neutron-scattering data for the equilibrium occupation of electronic bands. We find the effect of phonon softening by the electron-hole plasma to be substantially larger in the optical modes than in the acoustic modes throughout the Brillouin zone.