Wave functions andgfactor of holes in Ge/Si quantum dots

Abstract

We investigate theoretically the Zeeman effect on the hole states in quantum dots. In frame of tight-binding approach, we propose a method of calculating the g factor for localized states. The principal values of the g factor for the ground hole state in the self-assembled Ge/Si quantum dot are calculated. We find the strong g-factor anisotropy---the components ${g}_{\mathrm{xx}},$ ${g}_{\mathrm{yy}}$ are one order smaller than the ${g}_{\mathrm{zz}}$ component, ${g}_{\mathrm{zz}}=12.28,$ ${g}_{\mathrm{xx}}=0.69,$ ${g}_{\mathrm{yy}}=1.59.$ The efficiency of the developed method is demonstrated by calculating of the size dependence of g factor and by establishment of the connection with two-dimensional case. The g-factor anisotropy increases with the size of the quantum dot. The analysis of the wave function structure shows that the g factor and its size dependence are mainly controlled by the contribution of the state with ${J}_{z}=\ifmmode\pm\else\textpm\fi{}\frac{3}{2},$ where ${J}_{z}$ is the angular momentum projection on the growth direction of the quantum dot.