Pattern of charge ordering in quasi-one-dimensional organic charge-transfer solids

Abstract

We examine two recently proposed models of charge ordering (CO) in the nominally 1 4 -filled, quasione-dimensional (1D) organic charge transfer solids (CTS). The two models are characterized by site charge density "cartoons" ...1010... and ...1100..., respectively. We use the Peierls-extended Hubbard model to incorporate both electron-electron (e-e) and electron-phonon (e-ph) interactions. We first compare the results, for the purely electronic Hamiltonian, of exact many-body calculations with those of Hartree-Fock (HF) mean field theory. We find that HF gives qualitatively and quantitatively incorrect values for the critical nearest-neighbor Coulomb repulsion (Vc) necessary for ...1010... order to become the ground state. Second, we establish that spin-Peierls (SP) order can occur in either the ...1100... and ...1010... states and calculate the phase diagram including both on-site and intra-site e-ph interactions. Third, we discuss the expected temperature dependence of the CO and metal-insulator (MI) transitions for both ...1010... and ...1100... CO states. Finally, we show that experimental observations clearly indicate the ...1100... CO in the 1:2 anionic CTS and the (TMTSF)2X materials, while the results for (TMTTF)2X with narrower one-electron bandwidths are more ambiguous, likely because the nearest neighbor Coulomb interaction in these materials is near Vc.

Phase diagram of the one-dimensional Hubbard-Holstein model at half and quarter filling

“…considered here. 39,40 In addition, the pattern of the BOW ͑the location of the "strong" bond͒ coexisting with the¯1100¯CDW also depends on the strength of V. 39 If a similar metallic phase exists adjacent to the¯1100¯CDW, it is possible that a region of nearest-neighbor superconducting pairing found may be relevant to real quarter-filled molecular superconductors.…”

“…As quarter filling is commensurate, a Peierls state is also expected to occur for sufficiently large g. There are, however, significant differences between half-filled and quarter-filled Peierls states. At quarter filling, there are more than one possible pattern of charge and bond distortion, and which one actually occurs depends on the values of U as well as V. 39,40 In the absence of phonons, the quarter-filled band for finite U is a LL with neither charge nor spin gaps. At half filling, ͑2k F ͒ and ͑2k F ͒ are degenerate at U =0 ͑note that 2k F = /2 at quarter filling and corresponds to a correlation function with period 4 in real space͒.…”

Paired electron crystal: Order from frustration in the quarter-filled band

“…α ν is the inter-site e-p coupling constant, K ν α is the corresponding spring constant, and ∆ ij is the distortion of the bond between sites i and j. v i is the intra-site phonon coordinate and β is the intra-site e-p coupling with corresponding spring constant K β . Both ∆ ij and v i are determined self-consistently 57 . α ν are in general taken close to the minimum value needed for the transition to occur, our goal being the replication of the same instability from finite cluster calculations that would occur in the infinite system for 0 + coupling.…”

Magnetism in BEDT-TTF materials

“…This could be because of our ignoring electron-lattice interactions in the Hamiltonian (2). As shown elsewhere, such interactions cause strong modulations of the hopping integrals in the presence of CO in the 1/4-filled lattices [6,7]. It is possible that in the real materials, the differences in CO are too small for easy detection, but the resultant hopping integral modulations are large and reduce frustration.…”

“…Mean field (Hartree/Hartree-Fock) calculations are often cited as correctly reproducing the experimental magnitude of the AFM moment [3]. It is, however, well known that mean field theory greatly exaggerates broken symmetry in correlated systems: for example Hartree-Fock incorrectly predicts long-range AFM in one dimension (1D), and gives qualitatively incorrect predictions for charge order (CO) in 1D as well as 2D [6,7].…”