Identifying the Genes of Unconventional High Temperature Superconductors

We elucidate a recently emergent framework in unifying the two families of high temperature (high $T_c$) superconductors, cuprates and iron-based superconductors. The unification suggests that the latter is simply the counterpart of the former to realize robust extended s-wave pairing symmetries in a square lattice. The unification identifies that the key ingredients (gene) of high $T_c$ superconductors is a quasi two dimensional electronic environment in which the d-orbitals of cations that participate in strong in-plane couplings to the p-orbitals of anions are isolated near Fermi energy. With this gene, the superexchange magnetic interactions mediated by anions could maximize their contributions to superconductivity. Creating the gene requires special arrangements between local electronic structures and crystal lattice structures. The speciality explains why high $T_c$ superconductors are so rare. An explicit prediction is made to realize high $T_c$ superconductivity in $Co/Ni$-based materials with a quasi two dimensional hexagonal lattice structure formed by trigonal bipyramidal complexes.