Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.

state would have an infinite lifetime within the electric-dipole approximation,because the emitted photon cannot carry an angular momentum of 2. However,the dark exciton can recombine via LO-phonon-assisted, momentumconservingtransitions [39]. Spherical LO phonons with orbital angularmomenta of 1 or 2 are expected to participate in these transitions; the selectionrules are determined by the coupling mechanism [12,22]. Consequently, forzero field, the LO phonon replicas are strongly enhanced relative to the ZPL.With increasing magnetic field, however, the F2 level gains an optically activeF1 character [Eq. (42)], diminishing the need for the LO-phonon-assistedrecombination in dots for which the hexagonal axis is not parallel to themagnetic field. This explains the dramatic increase in the ZPL intensityrelative to LO phonon replicas with increasing magnetic field.The magnetic-field-induced admixture of the optically active F1 statesalso shortens the exciton radiative lifetime. Luminescence decays for 12-A˚ -radius NCs between 0 and 10 T at 1.7 K are shown in Fig. 8b. The sample wasexcited far to the blue of the first absorption maximum to avoid orientationalselection in the excitation process. Excitons rapidly thermalize to the groundstate through acoustic and optical phonon emission. The long microsecondluminescence at zero field is consistent with LO-phonon-assisted recombinationfrom this ground state. Although the light emission occurs primarilyfrom the F2 state, the long radiative lifetime of this state allows the thermallypopulated F1 L state to contribute to the luminescence also.With increasing magnetic field, the luminescence lifetime decreases;because the quantum yield remains essentially constant, we intepret this resultas due to an enhancement of the relative rate. The magnetic field dependenceof the luminescence decays can be reproduced using three-level kinetics withF1 L and F2 emitting states [2]. The respective radiative rates from thesestates, G 1 (h H , H ) and G 2 (h H , H ), in a particular NC, depend on the angle h Hbetween the magnetic field and the crystal hexagonal axis. The thermalizationrate, G th of the F1 L state to the F2 level is determined independently frompicosecond time-resolved measurements. The population of the F1 L level isdetermined by microscopic reversibility. We assume that the magnetic fieldopens an additional channel for ground-state recombination via admixture inthe F2 state of the F1 states: G 2 (h H , H ) = G 2 (0, 0) + 1/s 2 (h H , H ). This alsocauses a slight decrease in the recombination rate of the F1 L state.The decay at zero field is multiexponential, presumably due to sampleinhomogeneities (e.g., in shape and symmetry-breaking impurity contaminations).We describe the decay using three three-level systems, each having adifferent value of G 2 (0, 0) and each representing a class of dots within theinhomogeneous distribution. These three-level systems are then weighted toreproduce the zero field decay (Fig. 8c). We obtain average values of 1/G 2 (0, 0)= 1.42 ls and 1/G 1 (0, 0) = 10.0 ns. The latter value is in a good agreementCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.