Abstract: The properties of the magnetopolaron in an asymmetry quantum well is studied within Pekar variation method and unitary transformation method. The magnetopolaron ground state energy is obtained by theoretical derivation. The relations between the ground state energy of the magnetopolaron and the well width , the wave vector and the magnetic field cyclotron resonance frequency are further discussed by us. Due to the crystal structural inversion asymmetry and the magnetic field, the polaron energy occurs Rashba spin-orbit splitting and Zeeman splitting. Under the strong and weak magnetic fields, we discussed the dominant position of Rashba effect and Zeeman effect, respectively. Due to the presence of phonons, the polaron is more stable than the bare electron state, and the energy splitting is more stable.

Key words: condensed matter physics, Rashba e?ect, Zeeman e?ect, magnetopolaron, asymmetry quantum well