  We analyze the empirical correlation between the zero temperature penetration
depth $\lambda_{c}(0) $ and the corresponding normal state DC conductivity
$\sigma_{c}^{DC}$, measured slightly above the transition temperature $T_{c}$,
in different classes of quasi two-dimensional superconductors, including
cuprates and organics. For this purpose we invoke the scaling theory of quantum
and finite temperature critical phenomena. Important implications are:
Superconductivity in the organic and cuprate superconductors is a genuine three
dimensional (3D) phenomenon. The competition between anisotropy and
superconductivity destroys the latter in the 2D limit even in the ground state.
The data uncovers the flow to quantum criticality, including the 2D quantum
superconductor to insulator (2D-QSI) and the 3D quantum superconductor to
normal state (3D-QSN) transition. This flow gives a clear perspective of the
regimes where quantum fluctuations are essential and mean-field treatments
fail. Thus, a detailed account of the flow from mean-field to 2D-QSI
criticality in organics and the crossover from the 2D-QSI to the 3D-QSN
critical point in cuprates is a challenge for microscopic theories attempting
to solve the puzzle of superconductivity in these materials.
