Emergence of Superconductivity, Valence Bond Order, and Mott Insulators in $\mathrm{Pd}[(\mathrm{dmit}{)}_2]$ Based Organic Salts

The ${\mathrm{EtMe}}_3\mathrm{P}$ and ${\mathrm{EtMe}}_3\mathrm{Sb}$ triangular organic salts are distinguished from other $\mathrm{Pd}[(\mathrm{dmit}{)}_2]$ based salts, as they display valence bond and no long-range order, respectively. Under pressure, a superconducting phase is revealed in ${\mathrm{EtMe}}_3\mathrm{P}$ 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 ${\mathrm{EtMe}}_3\mathrm{P}$ salt, where the reentrant transition of insulator-metal-insulator type can be explained by an entropy difference between the metal and U(1) spin liquid. We predict different temperature dependence of the specific heat between the spin liquid and metal.

Figure 1

The doubled unit cell and form factors $g_r^{\pm }(\overrightarrow{k})$.

Figure 2

The $J$ vs $U$ phase diagram. The dotted line denotes a second-order transition, while the solid line is first-order. The label $d+id$ denotes the superconducting phase, and the inset shows the phase of $\Delta$ on each bond. The U(1) spin liquid is labeled SL. The pattern of $\chi$ and $B$ in the VB ordered state is inset in the VB phase, with thick lines denoting large values and thin lines small values. We have rescaled $U\to U/2$ as discussed in 15.

Figure 3

Finite temperature phase diagrams, with $J=0.25$ for (a) and $J=0.00$ for (b). Curves have been fitted to the boundaries to guide the eye. A dotted line denotes a second-order transition, a solid line is first-order transition, and a dashed line is a crossover. Note the superconducting phase at small $U$ for $J=0.25$ in (a). In (c) specific heat as a function of $T$ is shown for various values of $U$ denoted by different colors in (b). Note that the slope of the curves increases with $U$ indicating more density of states in SL insulator than metal.