Self-energy of a confined polaron in a quantum well: Comparison among different phonon models

We study the interaction of an electron with the confined longitudinal optical phonons in quantum wells. For the Fröhlich interaction of the electron-phonons we adopt the Huang-Zhu [Phys. Rev. B 38, 2183 (1988); 38, 13 377 (1988)] confined phonon model based on a microscopic lattice-dynamic approach. The explicit expression for the electron self-energy is obtained using a variational method. We also use the slab model and the guided model for the confined optical phonons in calculating the electron self-energy. Consequently, a comparison of three models considered is provided.