Theory of pure dephasing and the resulting absorption line shape in semiconductor quantum dots

The pure dephasing of the optical polarization and the corresponding line shape of absorption spectra in small quantum dots due to the interaction of the exciton both with optical and acoustic phonons is calculated. By restricting ourselves to the exciton ground state we obtain a model which is known to be exactly solvable. We study the temperature dependence and the influence of a static electric field. The spectra exhibit strongly non-Lorentzian line shapes including a sharp zero-phonon line. Optical phonons lead to phonon sidebands which may acquire a finite width due to the dispersion of the phonon branch; the width increases with decreasing dot size. Acoustic phonons both due to deformation potential and piezoelectric coupling lead to a broad background in the spectra which is strongly temperature dependent. Typical features of the spectra are qualitatively well reproduced by a perturbative approach based on one-phonon processes. Multiphonon processes, however, give significant contributions in particular in the case of acoustic phonons. Lateral or vertical electric fields lead to an increasing efficiency of the polar interaction mechanisms while deformation potential interaction is much less influenced.