Antiferromagnetism and Superconductivity in Layered Organic Conductors: Variational Cluster Approach

The $\kappa \mathrm{\text{−}}(\mathrm{ET}{)}_{2}X$ layered conductors (where ET stands for BEDT-TTF) are studied within the dimer model as a function of the diagonal hopping $t^{\prime }$ and Hubbard repulsion $U$. Antiferromagnetism and $d$-wave superconductivity are investigated at zero temperature using variational cluster perturbation theory (VCPT). For large $U$, Néel antiferromagnetism exists for $t^{\prime }<t_{c2}^{\prime }$, with $t_{c2}^{\prime }\sim 0.9$. For fixed $t^{\prime }$, as $U$ is decreased (or pressure increased), a $d_{x^2-y^2}$ superconducting phase appears. When $U$ is decreased further, then a $d_{xy}$ order takes over. There is a critical value of $t_{c1}^{\prime }\sim 0.8$ of $t^{\prime }$ beyond which the AF and dSC phases are separated by the Mott disordered phase.

Figure 1

(a) Schematic view of the hopping terms in the dimer model. VCPT uses a tiling of clusters such as the 4-site cluster drawn here (dashed lines). (b) Qualitative phase diagram inferred from our calculations (not to scale). See text for details.

Figure 2

Pressure ($t/U$) dependence of the antiferromagnetic (blue triangles), $d_{x^2-y^2}$ (red circles, scaled by 2) and $d_{xy}$(green squares, scaled by 5) order parameter, obtained with VCPT on $2\times 2$ clusters, for various values of $t^{\prime }/t$. The vertical lines indicate the transition points, separating the various phases.

Figure 3

Same as Fig. 2, this time for $2\times 4$ clusters.

Figure 4

Energy distribution curves (i.e. spectral function) for three sample solutions with $t^{\prime }=0.8t$. (a) an antiferromagnetic solution at $U=9t$. The SDW dispersion curves for the same values of the parameters ($U$, $\mu$, $t^{\prime }$ and $t$) and a mean field $h=0.4t$ are also drawn. (b) the same, for a Mott insulator solution ($U=7t$). What looked like the AF gap in (a) is now a Mott gap. (c) the same, for a $d_{x^2-y^2}$ solution ($U=5t$). Notice the $d$-wave gap maximum along the $(0,0)-(0,\pi )$ segment. In all cases, a Lorentzian broadening of $0.15t$ has been used.