Bound polaron in a cylindrical quantum wire of a polar crystal

The impurity binding energy in a cylindrical quantum wire was studied by the variational approach. A two-parameter trial wave function was proposed to reflect the anisotropsy of the quantum wire. We have also derived the electron-phonon interaction Hamiltonians for the confined longitudinal optical phonon modes and the interface phonon (IO) modes in the cylindrical quantum wire. The influence of different phonon modes on the impurity binding energy was studied. Numerical calculation shows that the impurity binding energy increases greatly as the radius of the quantum wire decreases and is strongly modified by the electron-phonon interaction, especially by the electron-IO phonon interaction.