  We investigate the two-orbital periodic Anderson model, where the local
orbital fluctuations of f-electrons couple with a two-fold degenerate
Jahn-Teller phonon, by using the dynamical mean-field theory. It is found that
the heavy fermion state caused by the Coulomb interaction between f-electrons U
is largely enhanced due to the electron-phonon coupling g, in contrast to the
case with the single-orbital periodic Anderson model where the effects of U and
g compete to each other. In the heavy fermion state for large $U$ and g, both
the orbital and lattice fluctuations are enhanced, while the charge (valence)
and spin fluctuations are suppressed. In the strong coupling regime, a sharp
soft phonon mode with a large spectral weight is observed for small U, while a
broad soft phonon mode with a small spectral weight is observed for large U.
The cooperative effect of U and g for half-filling with two f-electrons per
atom $n_f=2$ is more pronounced than that for quarter-filling with $n_f=1$.

Strongly Correlated Electrons