The quantum Ettingshausen effect in parabolic quantum wells with in-plane magnetic field in the presence of laser radiation under the influence of confined optical phonon

Abstract

The quantum Etttingshausen e˙ect in a parabolic quantum well subjected to a constant electric field, magnetic field in the presence of laser radiation is studied by using the quantum kinetic equation method. The analytic expressions for conductivity tensors and dynamic tensors as well as the Ettingshausen coe˚cient (EC) are obtained in the case of the confined electron-confined optical phonon (COP) scattering. The EC depends on specific quantities for external field (such as magnetic field, amplitude and frequency of laser radiation), temperature of the system and quantum well length, especially quantum number m-characterizing the confinement of optical phonon (OP). When m is set to zero, we get the results corresponding to the case of unconfined OP. The analytic results are numerically evaluated and graphed for GaAs/AlGaAs parabolic quantum well. When examining the e˙ect of temperature, the EC has greater values due to the COP. Meanwhile, when quantum well length and amplitude of the laser radiation (LR) increase, the EC has greater values without the confinement of OP. Because of the approach of system to bulk semiconductor structure when the quantum well length approaches micrometer-size, the EC reaches constant. The quantum number m leads to the change of resonance peaks position within the change of the magnetic field and the frequency of LR. In addition, the EC exerts non-linear dependence on the amplitude the LR. All results indicated that the COP a˙ects not only qualitatively but also the transformation rules of the EC. It provides new insights and contributes to the orientation of research into quantum e˙ects in low-dimensional semiconductor systems (LDS).