Comparative study of organic metals and high-T$_c$ cuprates

The Bechgaard salts and the high T$_c$ cuprates are described by two and three band models, respectively, with the lowest band (nearly) half filled. In organics the interactions are small, while in cuprates the repulsion $U_d$ on the Cu site is the largest energy. The Mott AF state is stable in undoped materials in both cases. In the metallic phase of cuprates the $U_d\to\infty$ limit produces a moderate effective repulsion. The theories of the coherent SDW and charge-transfer correlations in the metallic phases of organics and cuprates are thus similar. In (undoped) organics those correlations are associated with commensurate $2k_F$ SDW and $4k_F$ bond or site modes. The corresponding modes in metallic cuprates are the incommensurate SDW and in particular O$_x$/O$_y$ quadrupolar charge transfer with wave vector $2q_{SDW}=q_0+G$. They are enhanced for dopings $x>0$, which bring the Fermi level close to the van Hove singularity. Strong coupling to the lattice associates the static incommensurate O$_x$/O$_y$ charge transfer with collinear "nematic" stripes. In contrast to organics, the coherent correlations in cuprates compete with local $d_{10}\leftrightarrow d_9$ quantum charge-transfer disorder.