Interchain coupling and the Peierls transition in linear-chain systems

We study the effect of interchain coupling on the Peierls transition temperature $T_P$ for a model with a nonplanar Fermi surface. Using the standard electron-phonon coupling, we show that the soft mode which causes the transition should have a wave vector $q_0=(\frac{\pi }{a}, \frac{\pi }{a}, 2p_F)$. We evaluate the effect of interchain coupling on $T_P$ within the mean-field theory, as well as the effect of fluctuations. Both these effects reduce $T_P$, but we find that there is a range of interchain coupling where this reduction, due to both effects, is small. Neutron-scattering cross section and fluctuation contribution to the specific heat are evaluated. Comparison is made with experiments on ${\mathrm{K}}_2$Pt${\mathrm{}\left(\mathrm{CN}\right)\mathrm{}}_4$ ${\mathrm{Br}}_{0.3}$·3${\mathrm{H}}_2$O (KCP) and tetrathiofulvalene-tetracyanoquinodimethan (TTF-TCNQ).