Response behavior of the two-chain Fermi gas

Abstract

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 $2{k}_{F}$ interchain Cooper pairing response is the most divergent as $T\ensuremath{\rightarrow}0$. The excitonic insulator response may also be important at high temperatures. For the single chain, either the $4{k}_{F}$ response or a four-particle $q=0$ response is the most divergent for strong coupling and repulsive ${g}_{1}$, depending upon the sign of ${g}_{2}\ensuremath{-}\frac{1}{2}{g}_{1}$. For the two-chain system, the most divergent response as $T\ensuremath{\rightarrow}0$ 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 $8{k}_{F}$ 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 ${g}_{1}=0$ may be crossed. We use these results to interpret the recent x-ray data on TTF-TCNQ showing a crossover from $4{k}_{F}$ to $2{k}_{F}$ behavior above the crossover from one-dimensional to three-dimensional behavior.