In Mike Norman's nice review of the theory of superconductivity in the cuprates he states:
The RVB spin gap was probably the first prediction for the subsequently observed pseudogap phase. In RVB theory, the pseudogap phase corresponds to a spin singlet state (with its resulting spin gap) but no phase coherence in the charge degrees of freedom. One of the interesting ideas to emerge from this was an explanation for transport in this phase, which reveals a metallic behavior for in-plane conduction, but an insulating behavior for conduction between the planes. In the RVB picture, the metallic behavior is due to the fact that the holons can freely propagate. But to tunnel between the planes, the holons and spinons must recombine to form physical electrons, and this costs the spin gap energy, thus one obtains insulating like behavior for the c-axis conduction (Lee, Nagaosa, Wen, 2006). This “gap” has now been directly seen in c-axis infrared conductivity data (Homes et al., 1993).
However, it seems to me that there is now an alternative hypothesis to explain the c-axis infrared conductivity data, which does not require this exotic recombination of holons and spinons into an electron. This is provided by a paper by Michel Ferrero, Olivier Parcollet, Gabriel Kotliar, and Antoine Georges, discussed in this earlier post. The difference between in plane and interplane transport arises simply from the wavevector dependence of the interplane hopping matrix element. But, the observed gap is still due to the pseudogap.
It seems to me that the two explanations you mention for the interlayer insulator are similar.
ReplyDeleteIn the Ferrero et. al. picture, the k-dependence of the interlayer hopping element has the effect of emphasizing the antinodal electrons' contribution to c-axis current (i.e. of suppressing the Fermi arc contribution). But since insulating behaviour results from the pseudogap, it could still be viewed as a consequence of the required recombination of hole and spin. Also, since the pseudogap vanishes at nodes, insulating behaviour that results from the pseudogap could only be expected if SOMETHING were suppressing the nodal current (even without Fermi arcs, the nodes themselves would give a semi-metallic contribution). So a k-dependent hopping element does not, as I undestand, move you away from the RVB picture of the interlayer insulator.
Maybe the Ferrero et. al. predictions for in-layer current are different, however, from RVB. That is, ff the former relies on a small density of electrons (on the arcs) to carry current while the latter can draw on a large population of ungapped holons.