Doped Valence Bond Solid and Superconductivity on the Shastry-Sutherland Lattice

Motivated by recent experiments on SrCu$_2$(BO$_3$)$_2$, we present a theoretical framework for understanding the ground states of the doped Mott insulator on the Shastry-Sutherland lattice. To provide a unified theoretical framework for both the valence bond solid state found in undoped SrCu$_2$(BO$_3$)$_2$ and the doped counterpart in on-going experimental pursuit, we analyzed the $t$-$J$-$V$ model via the bond operator formalism. The interplay between strong dimerization and the nearest-neighbor repulsive interaction leads to different behaviors of the doped holes determining the overall phase diagram. Specifically, if the nearest-neighbor repulsive interaction, $V$, is smaller than a critical value, $V_c$, the hole-pairing within dimers is preferred, resulting in the $S$- wave superconductivity at any non-zero $x$. On the other hand, if $V$ is larger than $V_c$, the density of paired-holes within the same dimers vanishes at finite $x$ and the plaquette $D$-wave superconductivity with a peculiar spatial pattern emerges. Implications to future experiments are discussed.