  Motivated by the remarkable experimental realizations of $f$-electron
superlattices, e.g. CeIn$_3$/LaIn$_3$- and CeCoIn$_5$/YbCoIn$_5$-
superlattices, we analyze the formation of heavy electrons in layered
$f$-electron superlattices by means of the dynamical mean field theory. We show
that the spectral function exhibits formation of heavy electrons in the entire
system below a temperature scale $T_0$. However, in terms of transport, two
different coherence temperatures $T_x$ and $T_z$ are identified in the
in-plane- and the out-of-plane-resistivity, respectively. Remarkably, we find
$T_z < T_x \sim T_0$ due to scatterings between different reduced Brillouin
zones. The existence of these two distinct energy scales implies a crossover in
the dimensionality of the heavy electrons between two and three dimensions as
temperature or layer geometry is tuned. This dimensional crossover would be
responsible for the characteristic behaviors in the magnetic and
superconducting properties observed in the experiments.
