Zeeman effect for holes in a Ge/Si system with quantum dots

The tight binding approximation is employed to study the Zeeman effect for the hole ground state in a quantum dot. A method is proposed for calculating the g factor for localized states in a quantum dot. This method can be used both for hole states and for electron states. Calculations made for a Ge/Si system with quantum dots show that the g factor of a hole in the ground state is strongly anisotropic. The dependence of the g factor on the size of a germanium island is analyzed and it is shown that anisotropy of the g factor increases with the island size. It is shown that the value of the g factor is mainly determined by the contribution of the state with the angular momentum component Jz=±3/2 along the symmetry axis of the germanium island.