Phonon softening and double-well potential formation due to electron-phonon interaction in heavy-fermion systems

We investigate the periodic Anderson-Holstein model by using the dynamical mean-field theory combined with the exact diagonalization method. For the strong electron-phonon coupling $g\simg g_c$, the system shows an anomalous heavy-fermion behaviour which is accompanied by a large lattice fluctuation and an extreme phonon softening. We also calculate an effective potential for the ions and find that a simple harmonic potential for $g\siml g_c$ changes into a double-well potential for $g\simg g_c$. The effective pairing interaction between the conduction electrons shows a maximum at $g \approx g_c$ where the superconducting transition temperature is expected to be maximum.