Förster energy transfer of dark excitons enhanced by a magnetic field in an ensemble of CdTe colloidal nanocrystals

We present a systematic experimental study along with theoretical modeling of the energy transfer in an ensemble of closely-packed CdTe colloidal nanocrystals identified as the F\"orster resonant energy transfer (FRET). We prove that at low temperature of 4.2 K, mainly the ground dark exciton states in the initially excited small-size (donor) nanocrystals participate in the dipole-dipole FRET leading to additional excitation of the large-size (acceptor) nanocrystals. The FRET becomes possible due to the weak admixture of the bright exciton states to the dark states. The admixture takes place even in zero magnetic field and allows the radiative recombination of the dark excitons. An external magnetic field considerably enhances this admixture, thus increasing the energy transfer rate by a factor of 2-3 in a field of 15T, as well as the radiative rates of the dark excitons in the donor and acceptor nanocrystals. The theoretical modeling allows us to determine the spectral dependence of the probability for the NC to serve as a donor for larger nanocrystals, to evaluate the energy transfer rates as well as to predict their dependencies on the magnetic field, to describe the spectral shift of the photoluminescence maximum due to the energy transfer and to reproduce the experimentally observed spectral dependencies of the photoluminescence recombination dynamics in the magnetic field.