Competition between anisotropy and superconductivity in organic and cuprate superconductors

We analyze the empirical correlation between the zero-temperature penetration depth λ_c(0) and the corresponding normal-state DC conductivity σ_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.