Bond patterns and charge-order amplitude in quarter-filled charge-transfer solids

Most quasi-one-dimensional (quasi-1D) quarter-filled organic charge-transfer solids (CTS) with insulating ground states have two thermodynamic transitions: a high-temperature metal-insulator transition followed by a low-temperature magnetic transition. This sequence of transitions can be understood within the 1D Peierls-extended Hubbard (PEH) model. However, in some quasi-1D CTS both transitions occur simultaneously in a direct metal to spin-gapped insulator transition. In this second class of materials the organic stack bond distortion pattern does not follow the pattern of a second dimerization of a dimer lattice. These materials also display charge ordering of a large amplitude below the transition. Using quantum Monte Carlo methods we show that the same PEH model can be used to understand both classes of materials, however, within different parameter regions. We discuss the relevance of our work to experiments on several quarter-filled conductors, focusing in particular on the materials (EDO-TTF)${}_{2}X$ and (DMEDO-TTF)${}_{2}X$.

Figure 1

Bond distortion patterns coexisting with $\cdots 1100\cdots$ CO in the quarter-filled band. Filled (unfilled) circles indicate molecules with charge density $0.5+\delta$ $\left(0.5-\delta \right)$. (a) BCDW2 with bond distortion pattern strong-medium-weak-medium (SMWM). The double line indicates a stronger bond (S) than a single line (M), and solid lines indicate bonds stronger than dashed lines (W). The arrows indicate charge transfer paths which influence the relative strength of the 1-1 and 1-0 bonds (see Sec. 2b). (b) BCDW1 with pattern strong-weak-strong-${\mathrm{weak}}^{\prime }$ $\left({\mathrm{SWSW}}^{\prime }\right)$. The single (S) bond is strongest, followed by double dashed $\left({\mathrm{W}}^{\prime }\right)$ and single dashed (W). (c) Schematic evolution with increasing nearest-neighbor Coulomb repulsion $V$ from $\text{BCDW}2\to$ $\text{BCDW}1\to$ $4k_{\mathrm{F}}$ CO. For moderate $V$, Coulomb repulsion of the neighboring charge-rich sites strengthens the BCDW1 bond distortion (see text).

Figure 2

Crossover between BCDW1 and BCDW2 in the limit of zero $e\text{−}p$ interactions (a) $R={\chi }_B\left(4k_{\mathrm{F}}\right)/{\chi }_B\left(2k_{\mathrm{F}}\right)$ as a function of $V$ with $U=6.25$. Circles, diamonds, triangles, and squares are for 32, 48, 64, and 96 site chains, respectively. Systems with $R$ below the horizontal line $R=1$ will distort in the BCDW2 bond pattern. The inset shows the finite-size scaling of $V_{R=1}$, the $V$ for which $R=1$.

Figure 3

Zero-temperature phase diagram of Eq. (1) in the limit of $0^{+}$ $e\text{−}p$ interactions at quarter filling. Open points are the crossover boundary between the BCDW2 and BCDW1 regions. Solid diamonds and solid lines mark the boundary to the $4k_{\mathrm{F}}$ CO region (see Ref. [13]). The $V=\frac{U}{2}$ line indicates the region of physical relevance for organic CTS.

Figure 4

$2k_{\mathrm{F}}$ charge susceptibility as a function of $U$ for a 48-site chain with $V=U/4,\alpha =g=0$, and inverse temperature $\beta =192$.

Figure 5

Results of self-consistent MPS calculations (see text). For all panels $V=U/4$. (a) Finite-size scaling of the charge-order amplitude $\mathrm{\Delta }n$ versus inverse chain length with $\alpha =1.2$ and $g=0$. Lines are linear fits. (b) Finite-size scaled $\mathrm{\Delta }n$ as a function of $U$ and $g$, with $\alpha =1.2$. (c) The overall amplitude of the bond distortion [see Eq. (2)] for the parameters of (b). In both (b) and (c) the filled (open) points correspond to BCDW2 (BCDW1) and lines are guides to the eye.

Figure 6

Hopping integrals for the same parameters as Fig. 5.

Figure 7

(a) Finite-size scaled $\mathrm{\Delta }n$ as a function of $U$ and $\alpha$ with $g=1.2$. (b) The overall amplitude of the bond distortion [see Fig. 5].

Figure 8

Hopping integrals for the same parameters as Fig. 7.