XVIth International Workshop on Quantum Systems in Chemistry and Physics 

Abstract 
RealTime TDDFT Simulation for Coherent Phonon Generation 
Yasushi Shinohara^{1}, Kazuhiro Yabana^{1,2}, JunIchi Iwata^{2}, Tomohito Otobe^{3} and George F. Bertsch^{4}
^{1}Graduate School for Pure and Applied Sciences, University of Tsukuba, Japan
^{2}Center for Computational Sciences, University of Tsukuba, Japan
^{3}Advanced Photon Research Center, Japan Atomic Energy Agency, Japan
^{4}Department of Physics, University of Washington, USA 
We have been developing a firstprinciples description for quantum dynamics of electrons and ions induced by an intense and ultrashort laser pulse. In our method, electron dynamics is described by the timedependent densityfunctional theory (TDDFT) solving the timedependent KohnSham equation in realtime, while the ion motion is described by classical mechanics with the force evaluated by the Ehrenfest theorem. We consider a dynamics under a spatiallyuniform electric field which includes the polarization field as well as the applied electric field. Our scheme is capable of describing dielectric function in the linear response regime [1]. It has also been applied to optical breakdown in nonlinear regime [2].
In my presentation, we report an application of our framework for coherent phonon generation in bulk Si [3]. Coherent phonon is a macroscopic lattice vibration induced by the ultrashort laser pulse whose duration is shorter than the vibration period.
The figure below shows the calculated force acting on optical phonon coordinate at photon frequencies of 2.25, 2.5 and 2.75 eV. In our calculation, direct band gap of bulk Si is 2.4 eV. When the laser frequency is below the direct band gap (2.25 eV, red solid line), the impulsive force is only seen during the irradiation of the laser pulse (016 fs). When the laser frequency is above the direct band gap (2.75 eV, blue dotted line), the force persists even after the laser pulse ends. These features are consistent with two mechanisms of coherent phonon generation which have been proposed in phenomenological studies, the impulsive stimulated Raman scattering (ISRS) and the diplacive excitation of coherent phonon (DECP). In the ISRS, the force is generated from virtual electronhole excitations. In the DECP, the force is generated from real electronhole excitations which persist even after the laser pulse ends. We thus conclude that, in our framework based on TDDFT, both mechanisms of ISRS and DECP are included in a unified way.
We also apply the method to semimetal, Sb. Preliminary results will be presented as well.
[1] G.F. Bertsch, J.I. Iwata, A. Rubio and K. Yabana, Phys. Rev. B 62, 7998 (2000)
[2] T. Otobe, M. Yamagiwa, J.I. Iwata, K. Yabana, T. Nakatsukasa and G.F. Bertsch, Phys. Rev. B 77,165104 (2008)
[3] Y. Shinohara, K. Yabana, Y. Kawashita, J.I. Iwata, T. Otobe and G.F. Bertsch, Phys. Rev. B 82, 155110 (2010)

Figure. The force on the optical phonon coordinate for three laser frequencies: 2.25 eV (red solid); 2.5 eV (green dashed); and 2.75 eV (blue dotted).



