Dimensional crossover in layered $f$-electron superlattices

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.