Effect of spin-orbit coupling on the structure of the electron ground state in silicon nanocrystals

The effect of spin-orbit interaction on the structure of the ground state in the conduction band of spherical silicon nanocrystals is theoretically studied using the envelope-function approximation and the $\mathbf{k}\cdot\mathbf{p}$ method. It is shown that the arising weak spin-orbit coupling of the conduction- and valence bands leads to specific asymmetric hybridization of the $s$- and $p$-type envelope functions with opposite spin orientations caused by the anisotropy of spin mixing in the silicon conduction band. As a result, the wave functions of the ground-state transform which is accompanied by an insignificant decrease in its energy. In this case, the spin-mixing parameter in nanocrystals depends strongly on their size due to the quantum-confinement effect.