Bound polaron in a cylindrical quantum wire of a polar crystal

The impurity binding energy in a cylindrical quantum wire was studied by th e variational approach. A two-parameter trial wave function was proposed to reflect the anisotropsy of the quantum wire. We have also derived the elec tron-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 ener gy was studied. Numerical calculation shows that the impurity binding energ y increases greatly as the radius of the quantum wire decreases and is stro ngly modified by the electron-phonon interaction, especially by the electro n-IO phonon interaction.