Enhanced Kondo Effect in an Electron System Dynamically Coupled with Local Optical Phonon

Abstract

We discuss Kondo behavior of a conduction electron system coupled with local optical phonon by analyzing the Anderson–Holstein model with the use of a numerical renormalization group (NRG) method. There appear three typical regions due to the balance between Coulomb interaction U_ee and phonon-mediated attraction U_ph. For U_ee>U_ph, we observe the standard Kondo effect concerning spin degree of freedom. Since the Coulomb interaction is effectively reduced as U_ee−U_ph, the Kondo temperature T_K is increased when U_ph is increased. On the other hand, for U_ee<U_ph, there occurs the Kondo effect concerning charge degree of freedom, since vacant and double occupied states play roles of pseudo-spins. Note that in this case, T_K is decreased with the increase of U_ph. Namely, T_K should be maximized for U_ee≈U_ph. Then, we analyze in detail the Kondo behavior at U_ee=U_ph, which is found to be explained by the polaron Anderson model with reduced hybridization of polaron and residual repulsive interaction among polarons. By comparing the NRG results of the polaron Anderson model with those of the original Anderson–Holstein model, we clarify the Kondo behavior in the competing region of U_ee≈U_ph.