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

TL;DR

This paper models topological strongly correlated superconductors with disorder on a triangular lattice, revealing conditions for high-temperature superconductivity and phase separation relevant to Cu-doped apatite, using a variational approach.

Contribution

It introduces a $t$-$J$-$U$ model analysis showing how disorder and correlations influence superconductivity and topology in Cu-doped apatite.

Findings

Superconductivity appears only for specific carrier concentrations.

Moderate bond disorder preserves topological properties with Chern number 2.

Room-temperature superconductivity is possible under certain exchange-to-hopping ratios.

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 $\mathrm{Pb_{10-\mathit{x}}Cu_\mathit{x}(PO_4)_{6}O}$. 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).