Prediction of a shape-induced enhancement in the hole relaxation in nanocrystals

We present a pseudopotential calculation of the single particle and excitonic spectrum of CdSe nanocrystals. We find that in the excitonic manifold derived from the ground state electron and the first 60 hole states there are two energy gaps much larger than the typical LO phonon energy in bulk CdSe. Such gaps can effectively slow down the hole relaxation process, as recently found experimentally. We show that they originate from two gaps in the hole spectrum and are therefore a single-particle effect, as opposed to an excitonic effect. The calculated width of the gaps increases with decreasing dot size in agreement with the experimental trend of the energy loss rate that decreases with dot size. We find that the presence of the gaps is not limited to CdSe nanocrystals with the wurtzite crystal structure but is also found in spherical InAs zinc-blende dots. Comparison with our results for quantum rods and cylinders of different aspect ratios, and with a single-band effective mass model, shows the origin of the gaps to be inter-band coupling in spherical NCs. The gaps disappear above an aspect ratio of about 3-4, thus predicting a fast hole relaxation for elongated nanostructures. PACS numbers: 71.15.-m, 71.55.-i