d-wave superconductivity in boson+fermion dimer models

We present a slave-particle mean-field study of the mixed boson+fermion quantum dimer model introduced by Punk et al. [Proc. Natl. Acad. Sci. USA 112, 9552 (2015)] to describe the physics of the pseudogap phase in cuprate superconductors. Our analysis naturally leads to four charge $e$ fermion pockets whose total area is equal to the hole doping $p$ for a range of parameters consistent with the $t\ensuremath{-}J$ model for high-temperature superconductivity. Here we find that the dimers are unstable to $d$-wave superconductivity at low temperatures. The region of the phase diagram with $d$-wave rather than $s$-wave superconductivity matches well with the appearance of the four fermion pockets. In the superconducting regime, the dispersion contains eight Dirac cones along the diagonals of the Brillouin zone.