  Correlations between electrons and the effective dimensionality are crucial
factors that shape the properties of an interacting electron system. For
example, the onsite Coulomb repulsion, U, may inhibit, or completely block the
intersite electron hopping, t, and depending on the ratio U/t, a material may
be a metal or an insulator. The correlation effects increase as the number of
allowed dimensions decreases. In 3D systems, the low energy electronic states
behave as quasiparticles (QP), while in 1D systems, even weak interactions
break the quasiparticles into collective excitations. Dimensionality is
particularly important for a class of new exotic low-dimensional materials
where 1D or 2D building blocks are loosely connected into a 3D whole. Small
interactions between the blocks may induce a whole variety of unusual
transitions. Here, we examine layered systems that in the direction
perpendicular to the layers display a crossover from insulating-like, at high
temperatures, to metallic-like character at low temperatures, while being
metallic over the whole temperature range within the layers. We show that this
change in effective dimensionality correlates with the existence or
non-existence of coherent quasiparticles within the layers.
