Electron g factor in one- and zero-dimensional semiconductor nanostructures

We investigate theoretically the Zeeman effect on the lowest confined elect ron in quantum wires and quantum dots. A general relation is established be tween the symmetry of a low-dimensional system and properties of the electr on g factor tenser, g(alpha beta). The powerful method used earlier to calc ulate the transverse g factor in quantum wells is extended to one-dimension al (1D) and OD zinc-blende-based nanostructures and analytical expressions are derived in the frame of Kane's model for the g factors in quantum wells , cylindrical wires, and spherical dots. The role of dimensionality is illu strated on two particular heteropairs, GaAs/A1(x)Ga(1-x)As and Ga1-xInxAs/I nP. The efficiency of the developed theoretical concept is demonstrated by calculating the three principal values of the g factor tenser in rectangula r quantum wires in dependence on the wire width to establish also the conne ction with the 2D case. [S0163-1829(98)01547-1].