Confinement of electrons in layered metals

We analyze the out of plane hopping in models of layered systems where the in--plane properties deviate from Landau's theory of a Fermi liquid. We show that the hopping term acquires a non trivial energy dependence, due to the coupling to in plane excitations, and can be either relevant or irrelevant at low energies or temperatures. The latter is always the case if the Fermi level lies close to a saddle point in the dispersion relation.