k⋅p finite-difference method: Band structures and cyclotron resonances of ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{S}\mathrm{b}/\mathrm{I}\mathrm{n}\mathrm{A}\mathrm{s}$ quantum wells

A simple theoretical six-band $\mathbf{k}\cdot \mathbf{p}$ finite difference method is developed and applied to calculate the electronic band structures and electronic Landau-level structures of the symmetric and asymmetric ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{S}\mathrm{b}/\mathrm{I}\mathrm{n}\mathrm{A}\mathrm{s}$ quantum wells (QW’s). The QW may exhibit a semiconductor-semimetal transition by changing the Al composition in the ${\mathrm{Al}}_x{\mathrm{Ga}}_{1-x}\mathrm{Sb}$ layer. The cyclotron-resonance splitting in the semiconducting structures is due to the large InAs conduction-band nonparabolicity and Zeeman effect. Broken-gap type-II semimetallic QW, in which the conduction-valence Landau-level mixing can yield a significant spin splitting for the InAs conduction-band Landau levels, produces a prominent electron double-line structure in the cyclotron-resonance spectra, whether the QW is symmetric or asymmetric. Strong oscillations in the electron cyclotron-resonance mass, amplitude, and linewidth are evident. The abnormal cyclotron-resonance mass jumps, amplitude minima, and linewidth maxima occurring near the even filling factors are due to the conduction-valence Landau-level mixing effect. These results are in good agreement with the experimental results.