The Origin of the Charge Ordering and Its Relevance to Superconductivity in $\theta$-(BEDT-TTF)$_2$X: The Effect of the Fermi Surface Nesting and the Distant Electron-Electron Interactions

TL;DR

This paper investigates the origin of charge ordering and its connection to superconductivity in organic compounds, highlighting the roles of Fermi surface nesting and distant electron-electron interactions through theoretical modeling.

Contribution

It demonstrates that charge ordering arises from Fermi surface nesting and long-range interactions, and explores the competition between different pairing symmetries in superconductivity.

Findings

Charge ordering is driven by Fermi surface nesting and distant interactions.

Some Fermi surface regions remain ungapped in the charge ordered state.

Superconductivity involves competing d-wave and p-wave pairing symmetries.

Abstract

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 $(3\times 3)\sim (3\times 4)$ 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 $3\times 3$ 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.