Five-fold way to new high Tc superconductors

Discovery of high Tc superconductivity in La2-xBaxCuO4 by Bednorz and Muller in 1986 was a breakthrough in the 75 year long search for new superconductors. Since then new high Tc superconductors, not involving copper, have also been discovered. Superconductivity in cuprates also inspired resonating valence bond (RVB) mechanism of superconductivity. In turn, RVB theory provided a new hope for finding new superconductors through a novel electronic mechanism. This article first reviews an electron correlation-based RVB mechanism and our own application of these ideas to some new noncuprate superconducting families. In the process we abstract, using available phenomenology and RVB theory, that there are five directions to search for new high Tc superconductors. We call them five-fold way. As the paths are reasonably exclusive and well-defined, they provide more guided opportunities, than before, for discovering new superconductors. The five-fold way are i) copper route, ii) pressure route, iii) diamond route, iv) graphene route and v) double RVB route. Copper route is the doped spin -1/2 Mott insulator route. In this route one synthesizes new spin -1/2 Mott insulators and dopes them chemically. In pressure route, doping is not external, but internal, a (chemical or external) pressure-induced self-doping suggested by organic ET-salts. In the diamond route we are inspired by superconductivity in boron-doped diamond and our theory. Here one creates impurity band Mott insulators in a band insulator template that enables superconductivity. Graphene route follows from our recent suggestion of superconductivity in doped graphene, a two-dimensional broadband metal with moderate electron correlations, compared to curates. Double RVB route follows from our recent theory of doped spin-1 Mott insulator for superconductivity in iron pnictide family. (author)