For many strongly correlated metals with layered crystal structure the temperature dependence of the interlayer resistance is different to that of the intralayer resistance. We consider a small polaron model which exhibits this behavior, illustrating how the interlayer transport is related to the coherence of quasiparticles within the layers. Explicit results are also given for the electron spectral function, interlayer optical conductivity, and the interlayer magnetoresistance. All these quantities have two contributions: one coherent ͑domi-nant at low temperatures͒ and the other incoherent ͑dominant at high temperatures͒. DOI: 10.1103/PhysRevB.68.081101 PACS number͑s͒: 71.38.Ht, 72.90.ϩy Many of the most interesting strongly correlated electron materials have a layered crystal structure and highly anisotropic electronic properties. Examples include the cuprates, 1 colossal magnetoresistance materials, 2 organic molecular crystals, 3,4 strontium ruthenate, 5 and cobalt oxides. 6 One poorly understood property is that the resistivity perpendicular to the layers can have quite a different temperature dependence to that parallel to the layers.7 This is in contrast to what is expected for an anisotropic Fermi liquid: the parallel and perpendicular resistivities then have the same temperature dependence, being determined by the intralayer scattering rate ⌫(T). In many of these materials the interlayer resistivity is a nonmonotonic function of temperature with a maximum at some temperature T Ќ max . In some of the materials the intralayer resistivity also has a maximum as a function of temperature, but at a higher temperature T ʈ max ϾT Ќ max . 2,4,5 An important question concerns how the interlayer transport is effected by the coherence ͑or existence͒ of quasiparticles within the layers.6,7 Recent angle-resolved photoemission spectroscopy ͑ARPES͒ experiments on two different layered cobalt oxide compounds 6 found that peaks were only observed in the electronic spectral function ͑cor-responding to coherent quasiparticle excitations within the layers͒ below a temperature T coh that was comparable to T Ќ max . Although many theoretical papers have considered the problem of interlayer transport ͑see Ref. 8 and references therein͒ we are unaware of any theory which starts with a many-body Hamiltonian and produces the three temperature scales T coh , T Ќ max , and T ʈ max .
9,10In this Rapid Communication we consider a simple microscopic model which elucidates the connection between interlayer transport and the coherence of quasiparticles. We find that the interlayer conductivity has two contributions. The coherent ͑incoherent͒ contribution is characterized by the intralayer momentum of the quasiparticle being ͑not being͒ conserved in the interlayer tunneling process and is dominant at low ͑high͒ temperatures. We show that experimentally the two different contributions could be clearly distinguished at finite frequencies or in a magnetic field parallel to the layers. The model is a layered version of Holstein's molecu...