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

One must also account for the influence of the magnetic field on the PLquantum efficiency of NCs. The PL quantum efficiency depends on the ratioof radiative (s r ) and nonradiative (s nr ) decay times. The magnetic fieldadmixes the dark- and bright-exciton states and shortens the radiative decaytime in NCs for which the hexagonal axis is not parallel to the magnetic field[see Eqs. (46) and (51)]. The PL quantum efficiency q(H, x) increases in NCswith hexagonal axis predominantly oriented orthogonal to the field. As aresult, the relative contribution of different NCs to the PL is also controlled byq(H, x) = [1 + s r (H, x)/s nr ]1 , where s r (H, x) in a strong magnetic field asdefined by Eq. (51). Thus, the polarization degree becomes [36]PðH; TÞ ¼ 2 m1 0 dx x tanhð0:5g ex;2l B HbxÞqðH; xÞm 1 0 dx ð1 þ xÞ2 qðH; xÞð61Þwhich reduces to Eq. (60) in the limit s nr >> s r , for which nonradiativetransitions are negligible.In the opposite limit of a low quantum efficiency (s nr < s r ) the maximumdegree of PL polarization is only 0.625 at low temperatures (this casecan be realized, e.g., in low fields for which the state mixing is weak). Thereduced degree of polarization is because NCs in which the hexagonal axis isperpendicular to the magnetic field are more emissive, but they have a zero gfactor. With increasing magnetic field, however, the radiative decay time s r isFigure 10 The nearly identical PL polarization in NCs of 40, 57, and 80 A˚ diameterfor magnetic fields up to 60 T at low temperatures along with the calculatedpolarization given by Eq. (4). Inset: Extracted values of g ex and s nr for these NCs.Copyright 2004 by Marcel Dekker, Inc. All Rights Reserved.