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

The normalization of a MCD by a SUM allows one to extract the absolute valueof a g factor.In the case for which the inhomogeneous line broadening is larger thanthe fine-structure exciton splitting, both the upper and lower exciton stateswith jFj = 1 contribute to the MCD signal. In addition, the F = 0 excitonstate contributes to the absorption and this contribution should be taken intoaccount in normalization of the MCD signal. The absorption coefficient of theF = 0 exciton states for r F polarized light depends also on the angle h betweenthe NC hexagonal axes and the light propagation direction:!a F 0 ðe e 0Þf NU 0pffiffiffiffiffisin 2 ðe e 0 Þ 2hexpð57Þ2p r0where N U 0 is the constant defined by Eq. (26), r 0 and e 0 ¼ e U 0 are the linewidthand the average energy, respectively, of the optically active F = 0 excitonstates for the given NC distribution.Assuming that the inhomogeneous broadening for all exciton states isthe same (r U 1 = r L 1 = r 0 = r) and is much larger than the exciton finestructuresplitting, we can obtain the following expression for the effectiveZeeman splitting of the S 3/2 1S e transition (after averaging over all solidangles):2r 2 0De ¼ l B H NU 1 gU ex;1 þ NL 1 gL ex;1N U 1 þ NL 1 þ NU 0 =4 ¼ l BHg effð58ÞThe magnitude of the MCD signal is proportional to the magnetic field and itsshape depends on the sign of the effective exciton g factor g eff .Experimental studies of CdSe NCs [35] show that the magnitude of theMCD signal for the 1S 3/2 1S e and 2S 3/2 1S e transitions increases linearly withmagnetic field. At the same time, the measured shape of the MCD signal forthese transitions was the reverse of each other and was described by thetheoretical normalized MCD curve with the positive and negative sizedependenteffective g factor, respectively ( g eff > 0 for the 1S 3/2 1S e transitionand g eff < 0 for the 2S 3/2 1S e transition). Equation (58) also gives oppositesigns for the effective exciton g factor for these two transitions; however, itdoes not reproduce the experimental size dependence of g eff [35]. The fact thatthe size dependence of the electron g factor was not taken into account incalculations might also be one of the possible reasons for this disagreement.F. Polarization of the PL in Strong Magnetic FieldsAn external magnetic field splits the ground dark-exciton state into twosublevels [see Eq. (38)]. The exciton sublevels are thermally populated if theCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.