$c$-axis resistivity and high-$T_c$ superconductivity

Recently we had proposed a mechanism for the normal-state $c$-axis resistivity of the high-$T_c$ layered cuprates that involved blocking of the single-particle tunneling between the weakly coupled planes by strong intraplanar electron-electron scattering. This gave a $c$-axis resistivity that tracks the $\mathrm{ab}$-plane $T$-linear resistivity, as observed in the high-temperature limit. In this work this mechanism is examined further for its implication for the ground-state energy and superconductivity of the layered cuprates. It is now argued that, unlike the single-particle tunneling, the tunneling of a bosonlike pair between the planes prepared in the BCS-type coherent trial state remains unblocked inasmuch as the latter is by construction an eigenstate of the pair-annihilation operator. The resulting pair delocalization along the $c$ axis offers energetically a comparative advantage to the paired-up trial state, and thus stabilizes superconductivity. In this scheme the strongly correlated nature of the layered system enters only through the blocking effect, namely, that a given electron is effectively repeatedly monitored (intraplanarly scattered) by the other electrons acting as an environment, on a time scale shorter than the interplanar tunneling time.