$d$-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 $t-J$ 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.

Figure 1

The boson+fermion quantum dimer model of Ref. [10]. (a) A particular dimer configuration. The lattice is shown in black. The bosonic dimers representing the valence bonds are shown in blue, whereas the spinful fermionic dimers representing a single electron delocalized over two sites are shown in green. (b) Diagrams representative of the various terms in the dimer Hamiltonian Eq. (2).

Figure 2

(a) Location of the band minima as a function of $T_3/T_1$ and $T_2/T_1$ (for $T_1=1$). The color scale corresponds to the distance along the $\mathrm{\Gamma }-M$ line in the Brillouin zone: Blue corresponds to the $\mathrm{\Gamma }$ point $k_x=k_y=0$, and red corresponds to the $M$ point $k_x=k_y=\pi$. The insets show contours of the dispersion of the lower band of the Hamiltonian Eq. (6) for specific choices of parameters in the corresponding regions. (b) Dominant superconductivity instability as a function of $T_3/T_1$ and $T_2/T_1$ for doping $p=0.25$ and $J=50$: $d$ wave (white) vs $s$ wave (black). Note the good correlation between the $d$-wave superconductivity and the appearance of four band minima.