C-axis Transport and Coupling

C-axis transport properties of cuprates are very anomalous and non-metallic. Experiments show that the interlayer tunneling is strongly blocked (or suppressed) due to strong electron-electron correlations. We (MT, A.J. Leggett) developed a model which describes the incoherent c-axis conductivity suppressed by the charge fluctuations. Without relying on any microscopic model of the normal state, the frequency and temperature dependence of the c-axis conductivity is calculated. The qualitative systematic agreement with experiments (away from well-developed "pseudogap phase") is found.

Several experimental facts show the importance of interlayer (or rather intra-bilayer) coupling (interaction and hopping): the intra-bilayer Josephson plasmon, the resonance neutron peak (odd symmetry with respect to the exchange of planes), and increase of T_c in bi-layers relative to single layers of the same family of cuprates (for some families). The understanding of the intra-bilayer hopping (e.g. bi-layer splitting of the Fermi surface) and intra-bilayer interaction is an important part of high-T_c puzzle.

Condensation energy

It has been proven to be extremely difficult to establish firmly not only a correct microscopic theory but also the essential correct Hamiltonian (not even to mention the description of the ground state and its excitations). But the important ingredients for the superconductivity can possibly be identified without understanding a whole range of new phenomena in cuprates (certainly, a range of problems for at least one decade).

The question is: which energy is lowered upon the superconducting transition? The analysis of spectroscopic experiments based on various sum rules can resolve some questions unambiguously.

Pseudogap and the third dimension

Pseudogap may or may not be connected with superconductivity. Pseudogap may or may not be revealing or helpful in our progress towards understanding of high-T_c superconductivity. But surely, it must be understood for consistent microscopic picture of cuprates. The role (if any) of the third dimension (c-axis direction) for the appearance of the pseudogap is investigated.