Cyclotron resonance of a magnetopolaron in a semiconductor quantum well

Taking into account the interactions of an electron with bulk longitudinal-optical (LO) phonons and surface-optical (SO) phonons, we study the cyclotron resonance of a magnetopolaron in a semiconductor quantum well by using the generalized Larsen perturbation method. Our results show that there appears, generally speaking, a complicated spectral splitting around phonon frequencies due to the fact that the SO-phonon frequency covers a range. In the experimentally interesting GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As sandwich structure, there are two branches of splitting cyclotron resonance spectral lines because the difference between the frequencies of bulk LO and SO phonons is negligibly small. In contrast to the confining-potential model, it is found that in a thin GaAs/${\mathrm{Ga}}_{1\mathrm{-}\mathrm{x}}$ ${\mathrm{Al}}_{\mathrm{x}}$As sandwich structure the polaron-mass correction increases with increasing well width.