High Temperature Superconductivity with Strong Correlations and Disorder: Possible Relevance to Cu-doped Apatite

Abstract

We examine the properties of topological strongly correlated superconductor with bond disorder on triangular lattice and demonstrate that our theoretical ($t$-$J$-$U$) model exhibits some unique features of the Cu-doped apatite $\mathrm{P}{\mathrm{b}}_{10-x}\mathrm{C}{\mathrm{u}}_x(\mathrm{P}{\mathrm{O}}_4{)}_6\mathrm{O}$. Namely, the paired state appears only for carrier concentration $0.8\lesssim n<1$ per Cu and is followed by a close-by phase separation into the superconducting and Mott insulating parts. Furthermore, a moderate amount of the bond disorder ($\Delta t/t\lesssim 20\%$) does not alter essentially the topology with robust Chern number $C=2$ which diminishes beyond that limit. A room-temperature superconductivity is attainable only for the exchange to hopping ratio $J/|t|\ge 1$ if one takes the bare bandwidth suggested by current DFT calculations. The admixture of $s$-wave pairing component is induced by the disorder. The results have been obtained within statistically consistent variational approximation (SGA).