Emergence of superconductivity, valence bond order and Mott insulators in Pd[(dmit)2] based organic salts

The $\EtMeP$ and $\EtMeSb$ nearly triangular organic salts are distinguished from most other Pd[(dmit)$_2$] based salts, as they display valence bond and no long range order, respectively. Under pressure, a superconducting phase is revealed in EtMe$_3$P near the boundary of valence bond order. We use slave-rotor theory with an enlarged unit cell to study competition between uniform and broken translational symmetry states, offering a theoretical framework capturing the superconducting, valence bond order, spin liquid, and metallic phases on an isotropic triangular lattice. Our finite temperature phase diagram manifests a remarkable resemblance to the phase diagram of the EtMe$_3$P salt, where the re-entrant transitions of the type insulator-metal-insulator can be explained by an entropy difference between metal and the U(1) spin liquid. We find that the superconducting pairing symmetry is $d \pm id$, and predict different temperature dependences of the specific heat between the spin liquid and metal.