Symplectic-Nt−Jmodel ands±superconductors

Abstract

The possible discovery of ${s}_{\ifmmode\pm\else\textpm\fi{}}$ superconducting gaps in the moderately correlated iron-based superconductors has raised the question of how to properly treat ${s}_{\ifmmode\pm\else\textpm\fi{}}$ gaps in strongly correlated superconductors. Unlike the case of the $d$-wave cuprates, the Coulomb repulsion does not vanish by symmetry, and a careful treatment is essential. Thus far, only weak-correlation approaches have included this Coulomb pseudopotential, which has motivated us to introduce a symplectic-$N$ treatment of the $t\ensuremath{-}J$ model that incorporates the strong Coulomb repulsion through the complete elimination of on-site pairing. Through a proper extension of time-reversal symmetry to the large-$N$ limit, symplectic $N$ allows, for the first time, a superconducting large-$N$ solution of the $t\ensuremath{-}J$ model. For $d$-wave superconductors, the previous uncontrolled mean-field solutions are reproduced, while for ${s}_{\ifmmode\pm\else\textpm\fi{}}$ superconductors, the $SU(2)$ constraint enforcing single occupancy acts as a pair chemical potential adjusting the location of the gap nodes. This adjustment can capture the wide variety of gaps proposed for the iron-based superconductors: line and point nodes, as well as two different, but related full gaps on different Fermi surfaces.