Charge ordering and local-singlet formation in quarter-filled band charge-transfer solids and oxides of early transition metals

In many 1/4-filled band nonsuperconducting charge-transfer solids (CTS), such as the θ-(ET)₂X and the "ladder" compounds (DT-TTF)₂Au(mnt)₂ a charge-ordering (CO) transition is followed by a transition to a spin-gap (SG) state. This phenomenon is of interest because (a) SG in dimensionality greater than 1 is relatively rare, and (b) similar SG transitions, preceded or accompanied by a CO transition, are also seen in 1/4-filled band oxides of early transition metals such as Ti ₄O₇ and α-NaV₂O₅. The mechanisms of the SG formations are not understood and are often controversial. We present a global perspective of the CO transitions in 1/4-filled band systems. We report calculations incorporating both electron-electron and electron-phonon interactions in 1/4-filled band (a) 1D chains (b) 2D rectangular and triangular lattices, and (c) zigzag and rectangular ladders. We show that CO in many 1/4-filled band materials involves the formation of "local dimers" or "intersite bipolarons" that are bound into a singlet state, thereby giving a SG. Our work presents a new mechanism for singlet formation in a wide variety of exotic semiconductors below the metal-semiconductor transition. We discuss the above CTS and oxides in the context of the theory, and speculate on the possible role of local dimers in the superconductivity observed in structurally related CTS and Ti- and V-oxides.