Effect of Impurity and Magnetic Field on the Ground-State Energy of Polaron in an Anisotropic Quantum Dot

We adopt an anisotropic quantum dot as the theoretical model and apply the linear combination operator method and variational technique to derive the ground state energy of the bound magnetic polaron. When subjected to an external magnetic field, the energy of the bound magnetopolaron experiences Zeeman splitting, which divides into two branches. Notably, the Zeeman splitting energy exhibits a linear proportionality to the magnetic field strength, and the corresponding energy gap expands with increasing field strength. Through numerical calculations, the dependencies of the ground state energy on critical parameters are analyzed, specifically the mean number of phonons, Coulomb binding potential strength, vibrational frequency, electron-phonon coupling strength, magnetic-field cyclotron frequency, transverse confinement strength, and longitudinal confinement strength. The findings reveal that the ground state energy decreases with the mean number of phonons, Coulomb binding potential strength, vibrational frequency and electron-phonon coupling strength. In contrast, it rises with the magnetic-field cyclotron frequency, as well as transverse and longitudinal confinement strengths. Since phonons and impurities lower the total energy of the system, polaron states exhibit greater stability compared to bare electron states.