Pair hopping mechanism of enhancement in $T_{c}$ for layered superconductors

Two body effective interactions coming from the quantum charge fluctuation may induce pairs tunneling between adjacent layers in high-Tc materials including cuprates, iron-pnictides, MgB$_{2}$, and MNX. This mechanism [1] is favored when 1) the one-body Hamiltonian shows negligible inter-layer single electron hopping for the 2D liquid around the Fermi level, and 2) unfilled extended orbitals support the pair tunneling via local two-electron scattering. Localized nature of the 2D liquid is essential. The density functional theory (DFT) can prove this picture in two steps. The Kohn-Sham scheme tells that the single-particle effective Hamiltonian possess these aspects most clearly for the highest $T_{c}$ material. The multi-reference generalization of DFT allows us to evaluate existence and relevance of the super pair tunneling. A possible mechanism for layered organic superconductors is also discussed. \\[4pt] [1] K. Kusakabe, J. Phys. Soc. Jpn., \textbf{78} (2009) 114716.