Initial Condition Sensitivity in Photoinduced Structural Phase Transitions – An Iterative Equation for Exciton Proliferation during Lattice Relaxation –

Abstract

We theoretically study lattice relaxation dynamics of photogenerated excitons, which proliferate during this relaxation, and finally result in a macroscopic excited domain in insulating solids. This macroscopic domain formation phenomenon is usually called “photoinduced structural phase transition (PSPT)”. According to recent experiments, occurrence or nonoccurrence of this PSPT is found to depend very sensitively on the way of the photoexcitation, even if the total absorbed photonic energy is same. It is nothing else but “initial condition sensitivity” peculiar to nonlinear systems. We concentrate our attention on this sensitivity, and investigate criticality of this proliferation, using an iterative equation for its time evolution. As one of the models describing such a sensitivity, we consider a 1-dimensional strongly coupled many exciton-Einstein phonon system interacting with a reservoir. In our system, excitons can proliferate through their third order anharmonicity. This anharmonicity originates from the long range Coulomb interaction among electrons and holes constituting excitons. Within the Markov approximation for the reservoir, the time evolution of the density matrix of this exciton-phonon system is investigated full-quantummechanically. In order to overcome numerical complexities, we solve our iterative equation for the proliferation by the following principle. We always focus only on the most front of the expanding photoinduced domain, and the contributions from the other excitons, not in this front, are approximated by a mean field. As the proliferation proceeds, this front moves. Accordingly, we, step by step, iterate this procedure till the excess phonon energy, initially given by the photoexcitation, is exhausted. Thus, we can investigate the whole process of the time evolution of the domain formation, until this domain contains a large number of excitons. As for the aforementioned initial condition sensitivity, we cast the difference of the initial conditions into the difference of the initial distance between adjacent photogenerated excitons. Net proliferation is concluded to occur only when this initial distance is moderate, being not too small nor too large. This sensitivity to the initial distance results from the aforementioned third order anharmonicity.