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

Abstract

The origin of the charge ordering in organic compounds θ-(BEDT-TTF)2X (X = M M ′ (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 (3 × 3) ∼ (3 × 4) 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 × 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 = M M ′ (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 =I3, in which superconductivity is experimentally observed. We find that there is a close competition between dxy-wave-like singlet pairing and px+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 θ-(BEDT-TTF)2X family, ranging from a charge ordered insulator to a superconductor.

Theoretical aspects of charge correlations in θ-(BEDT-TTF)2X

“…Moreover, even if the origin of the horizontal stripe in the Rb salt is the lattice distortion, the development of the horizontal stripe correlation at low temperatures in the Cs salt, where such a distortion has not been observed experimentally, remains puzzling. Related 9 to this point, Kuroki pointed out the possibility that the horizontal stripe charge correlation arises from the a-axis threefold correlation [30]. For the case of the Cs salt, although the nesting vector is close to (2/3, 1/3) f at high temperatures, it moves toward (3/4, 1/4) f (note that we are adopting the folded Brillouin zone scheme here) upon lowering the temperature as mentioned above.…”

“…There are several studies in which the pairing symmetry of superconductivity in X = I 3 has been discussed [28,30,33,43]. Since this superconductivity lies in the vicinity of the charge-ordering phase in Mori's electronic phase diagram (figure 1), one may expect the occurrence of unconventional superconductivity due to charge fluctuations.…”

“…For instance, in a model that considers electron-electron interactions up to nearest neighbors, the coexistence of spin and charge fluctuations results in competition between spin-singlet d x y -wave-like pairing and triplet f -wave-like pairing [28,33]. On the other hand, in the model that takes into account the next nearest neighbor interaction, the gap function can be more complicated [30]. Since it can be expected that the many body interactions do not depend strongly on the anions (although the band structure does), one must discuss the pairing symmetry for X = I 3 using a Hamiltonian with appropriate interactions that correctly reproduces the competition between the a-axis threefold and the horizontal stripe charge correlations in the case of Rb and Cs salts.…”

Infrared and Raman Studies of Charge Ordering in Organic Conductors, BEDT-TTF Salts with Quarter-Filled Bands

“…The electronic phase diagram of this family has been composed employing the dihedral angle φ between the adjacent BEDT-TTF molecules (See Figure 9), which is related to the bandwidth [74]. The dihedral angle was subsequently linked to t c /t p to explain the phase diagram, where t c and t p are the transfer integrals along the c (stacking) direction and a ± c (diagonal) directions forming a triangular lattice [75][76][77][78]. Watanabe discussed this phase diagram using t c /t p as follows [78].…”

Theories on Frustrated Electrons in Two-Dimensional Organic Solids

“…(a) IV characteristics of θ-ET 2 CsZn(SCN) 4 , adapted with permission from [83]; (b) Low temperature characters of the q 1 , q 1 and q 2 peaks of CsZn/Co and RbZn salts; (c) Time evolution of the X-ray intensities (peak and integrated ones) measured simultaneously with the resistivity, adapted with permission from [86], copyrighted by the Physical Society of Japan. Kuroki [89] made an attempt to explain the material-dependent wave numbers q 1 and q 1 (issue (3)) on the RPA basis, by introducing several extra V ij 's between those separated by two molecular spacing. He showed that the peak positions of the charge susceptibility χ c (q), which directly reflects the geometry of V (q) through W (q) in Equation (10), is sensitive in the chain direction, which reminds us of the degeneracy of chain stripes in the strong coupling theory.…”