Anti-Jahn–Teller disproportionation and prospects for spin-triplet superconductivity in $d$-element compounds

We argue that the unusual properties of a wide class of materials based on Jahn–Teller 3$d$- and 4$d$-ions with different crystal and electronic structures, from quasi-two-dimensional unconventional superconductors (cuprates, nickelates, ferropnictides/chalcogenides, ruthenate Sr$_2$RuO$_4$), manganites with local superconductivity to 3D ferrates (CaSr)FeO$_3$, nickelates RNiO$_3$ and silver oxide AgO with unusual charge and magnetic order can be explained within a single scenario. The properties of these materials are related to the instability of their highly symmetric Jahn-Teller “progenitors” with the ground orbital $E$-state to charge transfer with anti-Jahn–Teller disproportionation and the formation of a system of effective local composite spin-singlet or spin-triplet, electronic or hole bosons moving in a non-magnetic or magnetic lattice. These unusual systems are characterized by an extremely rich variety of phase states from non-magnetic and magnetic insulators to unusual metallic and superconducting states.