Influence of the spin-orbit split-off valence band on the hole g factor in semiconductor nanocrystals

We present results of k center dot p calculations of the effective g factor of holes confined in spherical, cube, and planar semiconductor nanocrystals (NCs). We use the six-band Luttinger model for semiconductors with the zinc-blende crystal structure and study the size dependence of the 8 top valence subband hole g factor caused by the admixture of the spin-orbit split-off valence subband 7. We present semianalytical expressions for the hole g factor which depends on the light- to heavy-hole effective mass ratio beta and on the ratio between spin-orbit energy splitting of valence band SO and the hole quantization energy Eh. The admixture of 7 states is significant for small SO/Eh and, in spherical and cube NCs, leads to a strong size dependence of the hole g factor. In thin planar nanoplatelets (NPLs) with infinite or large lateral sizes, the dependence of the heavy-hole g factor on NPL thickness is relatively weak. It is drastically enhanced and may become nonmonotonic in NPLs with finite in-plane sizes due to the additional hole states mixing. We discuss our results in comparison with published experimental data for CdSe- and InP-based spherical NCs and NPLs and point out the specificity of extracting hole g factor from the data measured on excitons.