Response behavior of the two-chain Fermi gas

We consider a model of TTF-TCNQ (tetrahiafulvalenium-tetracyanoquinodimethanide) and similar charge-transfer linear conductors in which there are two chains. The electrons on the acceptor (TCNQ) chains have a usual metallic band, but the electrons on the donor (TTF) chains have an inverted or "hole" band. The electrons on each chain interact via the forward and backward scattering $g_2$ and $g_1$ processes, respectively. Electrons on different chains interact via the analogous processes $W_2$ and $W_1$. The model is also applicable to two metallic chains, with the signs of $W_1$ and $W_2$ reversed. Using the techniques of Luther and Emery and of Chui and Lee we show that the problem may be mapped onto a similar problem of three coupled classical two-dimensional Coulomb gases. In addition to gaps in the spin degrees of freedom that were present in the single-chain problem, we find that the antisymmetric form of the resultant charge degrees of freedom may have a gap. We then investigate the predominant two-, four-, six-, and eight-particle response functions and calculate their temperature dependence. In addition to the four divergent two-particle response functions present in the single chain, there is a region for weak interaction strengths in which the $2k_F$ interchain Cooper pairing response is the most divergent as $T\to 0$. The excitonic insulator response may also be important at high temperatures. For the single chain, either the $4k_F$ response or a four-particle $q=0\mathrm{}$ response is the most divergent for strong coupling and repulsive $g_1$, depending upon the sign of $g_2-\frac{1}{2}{g}_1$. For the two-chain system, the most divergent response as $T\to 0$ for strongly attractive interactions ($g_1$ and $g_2$) is the response to the formation of excitonic "molecules" or exciton pairs. For strong coupling and repulsive $g_1$ either $8k_F$ or octet responses may be observable. We discuss these results in conjunction with our previous renormalization-group treatment, which indicates that for certain values of $g_2$, $W_2$, and $W_1$ the line $g_1=0\mathrm{}$ may be crossed. We use these results to interpret the recent x-ray data on TTF-TCNQ showing a crossover from $4k_F$ to $2k_F$ behavior above the crossover from one-dimensional to three-dimensional behavior.