Resonant Pair Tunneling and Singular effects of c-axis disorder in cuprates and organic superconductors

In the interlayer pair tunneling (ILPT) theory of superconductivity the large scale $T_c$ has its origin in the k-space locality of the inter layer pair tunneling matrix elements. We reinterpret the same physics as a process of resonant pair tunneling and illustrate it through cooper pair analysis. This interpretation is used to give a mechanism which leads to a singular suppression of $T_c$ as function of c-axis(off plane/axis) disorder. In this mechanism the non resonant tunneling processes arising from the c-axis disorder in general contributes a pair binding energy which is reduced by a factor $\frac{T_J}{\epsilon_F}$, where $T_J$ is the interlayer pair tunneling matrix element and $\epsilon_F$ is the fermi energy. This leads to a simple theorem which states that the scale of $T_c$ is controlled by the space average value of the bare one electron interlayer hoping matrix element. After briefly discussing that the ET and TMTSF molecule based organic superconductors are strongly correlated narrow band systems, the dramatic reduction of $T_c$ by anion disorder in organic superconductors is explained by our mechanism. Off plane disorder effects in some of the cuprates are also discussed