Landau levels and cyclotron resonance in graded mixed semiconductors

A mixed semiconductor crystal with graded composition is characterized by a position-dependent effective mass, which leads to an additional force acting on free carriers. Taking this force into account, the classical cyclotron motion of carriers is studied, and then the Landau levels are calculated for both $\overrightarrow{\mathrm{H}}\parallel \nabla m^{*}\left(\overrightarrow{\mathrm{r}}\right)$ and $\overrightarrow{\mathrm{H}}\perp \nabla m^{*}\left(\overrightarrow{\mathrm{r}}\right)$. The effective-mass gradient influences both the selection rules (allowing transitions with $\Delta n=\pm 2$) and the polarization dependence of cyclotron resonance.