Spin splitting of conduction subbands in III-V heterostructures due to inversion asymmetry

A formula for the spin splitting of conduction subbands in III-V heterostructures due to inversion asymmetry is derived and it is explicitly shown that the splitting is not proportional to the average electric field in the system. Calculated magnetic-field dependence of the splitting successfully describes the available experimental data for the ${\mathrm{In}}_{0.53}{\mathrm{Ga}}_{0.47}{\mathrm{A}\mathrm{s}/\mathrm{I}\mathrm{n}}_{0.52}{\mathrm{Al}}_{0.48}\mathrm{As}$ heterostructure. The theory of splitting for a magnetic field parallel to the interfaces is discussed in relation to the metal-insulator transition in two-dimensional systems.