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Nickel oxide superconductors offer an alternative playground forunderstanding the formation of Cooper pairs in correlated materials such as thefamous cuprates. By studying the La$_{n+1}$Ni$_n$O$_{2n+2}$ phase diagram onthe basis of hybrid and spin-polarized density functional theory simulations,we reveal the existence of charge and bond ordered (CBO) insulating phases thatare quenched by doping effects, ultimately resulting in a metallic phase at the$n=5$ member. Nevertheless, the phonons associated with the CBO identified inthe phase diagram remain sufficiently large to mediate Cooper pairs inLa$_6$Ni$_5$O$_{12}$, yielding a computed critical temperature between$T_c=11-19$ K consistent with the 13 K observed experimentally inNd$_6$Ni$_5$O$_{12}$. Thus, in order to identify the superconducting mechanism,extracting the relevant instabilities in the doping phase diagram ofsuperconductors appears critical.

Electron-phonon mediated superconductivity in R$_6$Ni$_5$O$_{12}$ nickel oxides