Pairing and Superconductivity Driven by Strong Quasiparticle Renormalization in Two-Dimensional Organic Charge Transfer Salts

We introduce and analyze a variational wave function for quasi-two-dimensional $\kappa \mathrm{\text{−}}(\mathrm{ET}{)}_2$ organic salts containing strong local and nonlocal correlation effects. We find an unconventional superconducting ground state for intermediate charge carrier interaction, sandwiched between a conventional metal at weak coupling and a spin liquid at larger coupling. Most remarkably, the excitation spectrum is dramatically renormalized and is found to be the driving force for the formation of the unusual superconducting state.

Figure 1

Single particle gap, ${\Delta }_0$ in units of the renormalized hopping $t^{*}$ (see text), and superconducting order parameter ${\psi }_{\mathrm{s}}$ as a function of $U/t$. For $U/t\lesssim 8.5$ the system is a Fermi liquid metal. Pairing and superconductivity build up in the intermediate coupling regime for $U/t\sim 8–10$ in a non-BCS fashion. While the pairing amplitude grows with $U/t$, superconductivity is nonmonotonic. For $U/t\gtrsim 10$, ${\psi }_{\mathrm{s}}$ is negligible and the system becomes a spin liquid. The inset shows a finite size analysis of ${\Delta }_0$ on lattices up to $22\times 22$ for $U=9.5t$. Extrapolating the results to large systems supports ${\Delta }_0>0$ for $L\to \infty$ (dashed line).

Figure 2

The renormalized hopping elements along the two diagonals (see right part of the inset) as a function of $U/t$. For $t^{\prime }=0.7t$, the diagonal $t^{\prime *}$ is strongly suppressed whereas $t^{\prime \prime *}$ is enhanced over their bare values (horizontal lines), suggesting a reorganization of the quasiparticle dispersion for $U\sim 8.5t$.

Figure 3

Contour plot of $|\nabla n_{\mathbf{k}}|$ for $U=0$ (left) and for $U/t=9$ (right). The strongly renormalized dispersion in the interacting case generates a fourfold symmetric structure. $|\nabla n_{\mathbf{k}}|$ is largest along the diagonals.

Figure 4

Spatial dependence of the spin-spin correlation function different $U$. For larger $U$ magnetic correlations along the two diagonals become indistinguishable even though the bare hopping elements are very different. The inset shows the $U/t$ dependence of the nearest neighbor spin correlation.