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A five-level {\Pp} model of the band structure for GaAs-type semiconductorsis used to describe the spin $g^*$-factor and the cyclotron mass $m^*_c$ ofconduction electrons in GaAs/Ga$_{1-x}$Al$_x$As quantum wells in an externalmagnetic field parallel to the growth direction. It is demonstrated that theprevious theory of the $g^*$-factor in heterostructures is inadequate. Ourapproach is based on an iteration procedure of solving 14 coupled differential{\Pp} equations. The applicability of the iteration procedure is verified. Thefinal eigenenergy problem for the conduction subbands is reduced to twodifferential equations for the spin-up and spin-down states of consecutiveLandau levels. It is shown that the bulk inversion asymmetry of III-V compoundsis of importance for the spin $g^*$-factor. Our theory with no adjustableparameters gives an excellent description of experimental data on the electronspin $g^*$-factor in GaAs/Ga$_{0.67}$Al$_{0.33}$As rectangular quantum wellsfor different well widths between 3 and 12 nm. The same theory describes verywell experimental cyclotron masses in GaAs/Ga$_{0.74}$Al$_{0.26}$As quantumwells for the well widths between 6 and 37 nm.Comment: 13 pages, 6 figures, to be published in PR

physical review. b, condensed matter and materials physics

Spin and cyclotron energies of electrons in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>GaAs</mml:mi><mml:mo>∕</mml:mo><mml:msub><mml:mi>Ga</mml:mi><mml:mrow><mml:mn>1</mml:mn><mml:mo>−</mml:mo><mml:mi>x</mml:mi></mml:mrow></mml:msub><mml:msub><mml:mi>Al</mml:mi><mml:mi>x</mml:mi></mml:msub><mml:mi>As</mml:mi></mml:mrow></mml:math>quantum wells

Spin and cyclotron energies of electrons inGaAs∕Ga1−xAlxAsquantum wells