The effect of an anisotropic confinement on the ground-state energy of a polaron in a parabolic quantum dot

We study the ground-state energy of a large polaron in a quantum dot. The electron is treated as trapped in an anisotropic parabolic box while the coupling to bulk LO phonons is considered. An upper bound to the ground-state energy of the polaron is obtained using the Fock approximation of Mart and Burkey. With this treatment, we obtain variational results that are good to describe weak or strong electron-phonon coupling as well as the isotropic and the one-and two-dimensional confinement limits. The usual asymptotic limits are found for all of these cases. Numerical calculations carried out in order to study the validity of each of these limits as a function of the degree of anisotropy are presented. Also we discuss the effect that the anisotropy and the strength of the confining potential have on the self-energy of the polaron. We find that an anisotropic confinement is more effective as regards increasing the self-energy of the polaron than an isotropic confinement.