The origin of the charge ordering and its relevance to superconductivity in θ-(BEDT-TTF)2X:: The effect of the fermi surface nesting and the distant electron-electron interactions

The origin of the charge ordering in organic compounds theta-(BEDT-TTF)(2)X (X=MM'(SCN)(4), M=Tl, Rb, Co, M'=Cs, Zn) is studied using an extended Hubbard model. Calculating the charge susceptibility within random phase approximation (RPA), we find that the (3x3)-(3x4) charge ordering observed at relatively high temperatures can be considered as a consequence of a cooperation between the Fermi surface nesting, controlled by the hopping integral in the c direction, and the electron-electron interactions, where the distant (next nearest neighbor) interactions that have not been taken into account in most of the previous studies play an important role. Mean field analysis at T=0 also supports the RPA results, and further shows that in the 3 x 3 charge ordered state, some portions of the Fermi surface remain ungapped and are nested with a nesting vector close to the modulation wave vector of the horizontal stripe ordering observed at low temperatures in X=MM'(SCN)(4). We further study the possibility of superconductivity by taking into account the distant off-site repulsions and the band structure corresponding to X=I-3, in which superconductivity is experimentally observed. We find that there is a close competition between d(xy)-wave-like singlet pairing and p(x+2y)-wave-like triplet pairing due to a cooperation between the charge and the spin fluctuations. The present analysis provides a possible unified understanding of the experimental phase diagram of the theta-(BEDT-TTF)(2)X family, ranging from a charge ordered insulator to a superconductor.