Microscopic theory of ultrafast processes in carbon nanomaterials

Abstract

We evaluate a density matrix theory for the description of ultrafast relaxation processes in low-dimensional carbon nanostructures. The theory is based on Bloch equations describing the temporal dynamics of charge carrier population and transition probabilities. In combination with tight-binding wavefunctions, the approach allows the microscopic calculation of linear and nonlinear optical properties of graphene and carbon nanotubes with arbitrary chirality. This way, we have access to time- and momentum-resolved relaxation dynamics of non-equilibrium charge carriers. We study absorption spectra in graphene and carbon nanotubes illustrating the importance of excitonic effects in these structures including the formation of exciton-phonon induced side-bands in carbon nanotubes. Furthermore, we illustrate the relaxation of optically excited charge carriers toward equilibrium via electron-phonon and electron-electron scattering. We observe an ultrafast thermalization of excited carriers within the first hundred femtoseconds followed by a cooling of the electronic system on the picosecond time scale. Moreover, we investigate phonon-induced intersubband relaxation between the two energetically lowest transitions in nanotubes leading to a better understanding of photoluminescence excitation (PLE) experiments.