Vibrational Frequency of Strong-coupling Impurity Bound Polaron in Quantum Rods

The Hamiltonian of a quantum rod with an ellipsoidal boundary is given after a coordinate transformation which can transform the ellipsoidal boundary into spherical one.The properties of the strong-coupling impurity bound polaron in a quantum rod in a three-dimensional anisotropic harmonic potential are studied by using the linear combination operator and the unitary transformation methods.The relationships among the vibrational frequency,the mean number of phonons of strong-coupling impurity bound polaron in a quantum rod and the Coulomb bound potential,the electron-phonon coupling strength,the aspect ratio of the ellipsoid and the transverse and the longitudinal effective confinement length of quantum rods were derived.Numerical calculations are performed and the results show that the vibrational frequency and the mean number of phonons increase the electron-phonon coupling strength and the Coulomb bound potential,decrease with the transverse and the longitudinal effective confinement length of quantum rods and the aspect ratio of the ellipsoid.These can be attributed to the interesting quantum size confining effects.