The electron g factor for one-band and two-band extended models of the electron energy spectrum

At present, explicit expressions for the electron g factor in crystals are known only for the following two cases: either the Fermi energy εF of the electrons lies at the edge of the electron energy band, ε(kex) , or the electron energy spectrum of a crystal can be approximated by the two-band model. Here we obtain explicit formulas for the g factor in situations when the Fermi level εF is close to but does not coincide with the band edge and when the two-band model of the spectrum includes small corrections from other electron energy bands. In particular, we derive the expressions that describe the dependences of the g factor on εF - ε(kex) and on the direction of the magnetic field for doped semiconductors. The results are applied to III-V semiconductors and to bismuth