Hole Zeeman effect in Ge/Si quantum dots

We investigate theoretically the Zeeman effect on the lowest confined hole in quantum dots. In frame of tight-binding approach we propose a method of calculating the Lande 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(xx), g(yy) are one order smaller, than the g(zz)-component, g(zz)=15.71, g(xx)=1.14, g(yy)=1.76. The efficiency of the developed method is demonstrated by calculating of size-dependence of g-factor and by establishment of the connection with 2D case. The g-factor anisotropy increases with the island and the ground hole state g-factor goes to heavy hole g-factor. The analysis of the wave function structure shows that g-factor and its size-dependence are mainly controlled by the contribution of the state with J(z)=+/-3/2.