Pattern of charge ordering in quasi-one-dimensional organic charge-transfer solids

Abstract

We examine two recently proposed models of charge ordering (CO) in the nominally $\frac{1}{4}$-filled, quasi-one-dimensional (1D) organic charge-transfer solids (CTS). The two models are characterized by site charge density ``cartoons'' $\dots{}1010\dots{}$ and $\dots{}1100\dots{},$ respectively. We use the Peierls-extended Hubbard model to incorporate both electron-electron $(e\ensuremath{-}e)$ and electron-phonon $(e\ensuremath{-}ph)$ interactions. We first compare the results, for the purely electronic Hamiltonian, of exact many-body calculations with those of Hartree-Fock (HF) mean-field theory. We find that HF gives qualitatively and quantitatively incorrect values for the critical nearest-neighbor Coulomb repulsion ${(V}_{c})$ necessary for $\dots{}1010\dots{}$ order to become the ground state. Second, we establish that spin-Peierls order can occur in either the $\dots{}1100\dots{}$ and $\dots{}1010\dots{}$ states and calculate the phase diagram including both on-site and intrasite $e\ensuremath{-}\mathrm{ph}$ interactions. Third, we discuss the expected temperature dependence of the CO and metal-insulator transitions for both $\dots{}1010\dots{}$ and $\dots{}1100\dots{}$ CO states. Finally, we show that experimental observations clearly indicate the $\dots{}1100\dots{}$ CO in the 1:2 anionic CTS and the $(\mathrm{TMTSF}{)}_{2}X$ materials, while the results for $(\mathrm{TMTTF}{)}_{2}X$ with narrower one-electron bandwidths are more ambiguous, likely because the nearest-neighbor Coulomb interaction in these materials is near ${V}_{c}.$