Slave fermion theory of confinement in strongly anisotropic systems

We present a mean field treatment of a strongly correlated model of electrons in a three–dimensional anisotropic system. The mass of the bare electrons is larger in one spatial direction (the c–axis direction), than in the other two (the ab–planes). We use a slave fermion decomposition of the electronic degrees of freedom and show that there is a transition from a deconfined to a confined phase in which there is no coherent band formation along the c–axis. One of the most controversial, and hard to understand, problems related with high-Tc cuprates is the anomalous charge transport observed experimentally. The charge dynamics reflects the anisotropy in the crystal structure of these compounds, which consists of weakly coupled planes. In the usual notation, we will refer to “c–axis” and “ab–planes” as the directions transverse and parallel to the planes respectively. The in–plane conductivity σab shows a behavior characteristic of the metallic state. On the other hand, close to the insulating state, in the so called underdoped regime, the c–axis conductivity σc is “incoherent”: the values of σc are below the minimum metallic conductivity , the temperature dependence is anomalous, and the frequency dependence does not show signatures of Drude–like behavior. Band structure calculations indicate an anisotropy which, within the framework of Boltzman transport, imply metallic behavior with an anisotropy σc/σab well above the experimental observation. Perturbative treatments within the Fermi–liquid theory indicate that the anisotropy is not renormalized by interactions. Perhaps the main objection to the “conventional” theories of c–axis transport is the observed value of the anisotropy of the conductivity. In the superconducting phase coherence is reestablished in all directions. This lead Anderson and others to attribute the anomalies in transport in the normal state to the effect of strong electronic correlations, and to conclude that in order to describe the incoherent c–axis conductivity the Fermi–liquid picture should be abandoned. The starting point used as a paradigm is the one-dimensional correlated problem where it is rigorously known that the Fermi–liquid picture fails. Considerable work has been done in weakly coupled chains that suggest that a state can be formed in which the coherence is confined to the motion along the chains, the motion transverse to the chains being incoherent.