Abstract

Ultra-fast optical spectroscopy is a powerful tool for the observation of dynamical processes in several kind of materials. The basic time-resolved optical experiment is the so-called “pump-probe” where a first light pulse, the “pump”, resonantly triggers a photo-induced process. The subsequent system evolution can be monitored, for example, by the time-dependent transmission changes of a delayed “probe” pulse. In a pump-probe experiment the pump pulse photon energy, spectral width and peak intensity creates a certain density of electron-hole pairs in a more or less localized region of space. After the creation of the initial carrier population the time evolution of the single-particle and many-particle excitations is now governed by a non-trivial interplay between electron-electron scatterings and energy relaxation.

In this talk I will present a novel approach based on the merging of Non-Equilibrium Green’s function theory and Density Functional Theory to investigate the dynamics following a pump excitation. I will first shortly discuss the general mathematical framework of the non-equilibrium theory based on a set of integro-differential equations (Hedin’s equations) written out-of-equilibrium. I will show how it is possible to include consistently quantized electron, photons and phonons. I will, then, take the purely longitudinal limit in order to introduce the key approximations that make the problem numerically treatable.

I will take the case of bulk silicon, a paradigmatic indirect gap semiconductor, to discuss the key features of the carrier dynamics. I will compare the results with recent two photon photoemission measurements. I will show that the interpretation of the carrier relaxation in terms of L->X inter-valley scattering is not correct. The ultrafast dynamics measured experimentally is, instead, due to the scattering between degenerate L states that is activated by the non symmetric population of the conduction bands induced by the laser field. This ultrafast relaxation is, then, entirely due to the specific experimental setup and it can be interpreted by introducing a novel definition of the quasi-particle lifetimes in an out-of-equilibrium context.