Spin and cyclotron energies of electrons in GaAs/Ga${}_{1-x}$Al${}_x$As quantum wells

Abstract

A five-level {\Pp} model of the band structure for GaAs-type semiconductors is used to describe the spin $g^{\ast }$-factor and the cyclotron mass $m_c^{\ast }$ of conduction electrons in GaAs/Ga${}_{1-x}$Al${}_x$As quantum wells in an external magnetic field parallel to the growth direction. It is demonstrated that the previous theory of the $g^{\ast }$-factor in heterostructures is inadequate. Our approach is based on an iteration procedure of solving 14 coupled differential {\Pp} equations. The applicability of the iteration procedure is verified. The final eigenenergy problem for the conduction subbands is reduced to two differential equations for the spin-up and spin-down states of consecutive Landau levels. It is shown that the bulk inversion asymmetry of III-V compounds is of importance for the spin $g^{\ast }$-factor. Our theory with no adjustable parameters gives an excellent description of experimental data on the electron spin $g^{\ast }$-factor in GaAs/Ga${}_{0.67}$Al${}_{0.33}$As rectangular quantum wells for different well widths between 3 and 12 nm. The same theory describes very well experimental cyclotron masses in GaAs/Ga${}_{0.74}$Al${}_{0.26}$As quantum wells for the well widths between 6 and 37 nm.

13 pages, 6 figures, to be published in PRB

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• Comment on ``Spin and cyclotron energies of electrons in GaAs/GaAlAs quantum wells''