Mean-Field Study of Charge Order with Long Periodicity in θ-(BEDT-TTF)₂X

Abstract

Charge ordering phenomenon in θ-(BEDT-TTF)2X is studied by using 1/4-filled extended Hubbard model on an anisotropic triangular lattice through mean-field approximation. It is found that a metallic charge ordered state with 3-periodicity on lattices (3-fold type charge order) is realized in the realistic parameter region where the nearest neighbor Coulomb interaction Vij is nearly isotropic. This 3-fold state survives up to high temperatures by estimating the free energy. Insulating state with diagonal or vertical-type charge ordering appears as increasing anisotropy of Vij. Considering the effect of the structural distortion observed in θ-(BEDT-TTF)2RbZn(SCN)4 at low temperatures, horizontal-type charge ordered insulating phase tends to be stabilized and the region where 3-fold type exists becomes narrower. Our results are consistent with the metallic state with long periodic charge order which can be related to 3-fold type in θ-(BEDT-TTF)2RbZn(SCN)4 at high temperatures and insulating state with horizontal charge order at low temperatures. For θ-(BEDT-TTF)2CsZn(SCN)4, we speculate several kinds of charge-ordered states are energetically competing with each other leading to an inhomogeneous state at low temperatures.

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

“…In Seo's calculation, the competition between the diagonal and horizontal stripe states was subtle, but the resulting effective spin Hamiltonian in the horizontal stripe phase is a quasi-one-dimensional Heisenberg chain along the p4 hopping integral, which explains the Bonner-Fisher type temperature dependence of the magnetic susceptibility [4,5]. From this viewpoint, Seo concluded that the horizontal stripe ordering is the most probable state in 4 In the theoretical studies of [25] and [35], the θ d lattice is not presented correctly, but the calculations are performed on the correct lattice. the insulating phase of X = RbM (SCN) 4 .…”

“…Following the line of Seo's study [15], Kaneko and Ogata [25] performed a mean-field analysis on the θ d lattice structure, where competition between the c-axis threefold state and the horizontal stripe was found to take place.…”

Geometrical frustration effects on charge-driven quantum phase transitions

“…32 More interesting from our perspective is the isotropically interacting case, V p = V c ≡ V . 20,28,29,[32][33][34][35][36] There, because of the frustration of intermolecular interactions induced by the triangular lattice geometry, an alternative charge-ordering pattern with threefold periodicity is favored with respect to the (degenerate) striped arrangements, illustrated in Fig. 1(b).…”

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

“…We will call this the "c-axis three-fold" charge ordering in the present paper. Later on, Kaneko and Ogata extended Seo's mean field study to take into account the possibility of this c-axis three-fold ordering, 20 where they found that this ordering does have a lower energy then the vertical, diagonal, and horizontal stripes when V p ∼ V c . In these studies, a possible relation between the c-axis three-fold ordering and the diffuse Xray spots observed at ( but quite recently, Hotta et al used exact diagonalization for a spinless half-filled model, which can be considered as an effective model of the θ-type compounds in the large on-site U limit, and showed the presence of c-axis three-fold charge correlation for V p ∼ V c .…”