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

where H z is the magnetic field projection alon the crystal hexagonal axis andH F = H x F iH y .A. Zeeman EffectOne can see from Eq. (37) that the magnetic field leads to Zeeman splittingof the double-degenerate exciton states. For the ground dark-exciton statewith angular momentum projection F2 this spliting, D e 2 = e 2 e 2 , can beobtained directly from Eq. (37):De 2 ¼ g cx;2 l B H cos h Hð38Þwhere g ex,2 = g e 3g h and h H is the angle between the nanocrystal hexagonalaxis and the magnetic field directions.Considering the magnetic field terms in Eq. (37) as a perturbation, wedetermine the Zeeman splitting of the optically active F = F1 state:De U 1 ¼ eU 1 e U 1 ¼ l BH z f½ðC þ Þ 2 ðC Þ 2 Šg e ½ðC þ Þ 2 þ 3ðC Þ 2 Šg h gDe L 1 ¼ eL 1 e L 1 ¼ l BH z f½ðC Þ 2 ðC þ Þ 2 Šg e ½ðC Þ 2 þ 3ðC þ Þ 2 Šg h gð39ÞThis splitting (linear in the magnetic field) is proportional to the magneticfield projection H z on the crystal hexagonal axis. Substituting Eq. (21) for C Finto Eq. (39), one can get the dependence of this splitting on the NC radius:De U;L1¼ g U;Lex;1 l BH cos h H ;wherepffiffiffiffiffiffiffiffiffiffiffiffiffig U ex;1 ¼ g f 2 fe pffiffiffiffiffiffiffiffiffiffiffiffiffig 2 þ d fh pffiffiffiffiffiffiffiffiffiffiffiffiffif 2 þ d f 2 þ dpffiffiffiffiffiffiffiffiffiffiffiffiffið40Þg L ex;1 ¼ g f 2 fe pffiffiffiffiffiffiffiffiffiffiffiffiffig 2 þ d þ fh pffiffiffiffiffiffiffiffiffiffiffiffiffif 2 þ d f 2 þ dThere is no splitting of the F = 0 optically active exciton state. In large NCs,for which one can neglect the exchange interaction (g D, g U ex,1 c ( g e + 5g h )/2and g L ex,1 c ( g e 3g h )/2. The average Zeeman splitting for a system of randomlyoriented crystals isDe U;Lex;1 ¼ gU;L ex;1 l BH; De ex;2 ¼ g ex;2l B H22for the F = F1 U,L and F = F2 states, respectively.ð41ÞCopyright 2004 by Marcel Dekker, Inc. All Rights Reserved.