Thermal properties of quantum transition process in piezoelectric materials based on the projected Liouville equation.

We study the temperature dependence of the Cyclotron Resonance absorption Line Shapes(CRLS) and the Cyclotron Resonance Line Widths(CRLW) in piezoelectric materials, CdS and GaAs. We examined theoretically the CRLS and CRLW in the quantum limit due to piezoelectric phonon scattering. We use the projected Liouville equation method approach. Trough the numerical calculation of the result of the theory, we find that the width increases with the temperature in two materials. We also find that the temperature dependence of the CRLW of the phonon emission process is more larger than the temperature dependence of the CRLW of the phonon absorption process.