From charge- and spin-ordering to superconductivity in the organic charge-transfer solids

We review recent progress in understanding the different spatial broken symmetries that occur in the normal states of the family of charge-transfer solids (CTS) that exhibit superconductivity (SC), and discuss how this knowledge gives insight to the mechanism of the unconventional SC in these systems. A great variety of spatial broken symmetries occur in the semiconducting states proximate to SC in the CTS, including charge ordering, antiferromagnetism and spin-density wave, spin-Peierls state and the quantum spin liquid. We show that a unified theory of the diverse broken symmetry states necessarily requires explicit incorporation of strong electron-electron interactions and lattice discreteness, and most importantly, the correct bandfilling of one-quarter, as opposed to the effective half-filled band picture that is often employed. Uniquely in the quarter filled band, there is a very strong tendency to form nearest neighbor spin-singlets, in both one-and two-dimension. The spin-singlet in the quarter-filled band is necessarily charge-disproportionated, with charge-rich pairs of nearest neighbor sites separated by charge poor pairs of sites in the insulating state. Thus the tendency to spin-singlets, a quantum effect, drives a commensurate charge-order in the correlated quarter-filled band. This charge-ordered spin-singlet, which we label as a paired-electron crystal (PEC), is different from and competes with both the antiferromagnetic (AFM) state and the Wigner crystal (WC) of single electrons. Further, unlike these classical broken symmetries, the PEC is characterized by a spin gap. The tendency to the PEC in two dimension is enhanced by lattice frustration. The concept of the PEC mirrors parallel development of the idea of a density wave of Cooper pairs in the superconducting high T-c cuprates, where also the existence of a charge-ordered state in between the antiferromagnetic and the superconducting phase has now been confirmed. Following this characterization of the spatial broken symmetries, we critically reexamine spin-fluctuation and resonating valence bond theories of frustration driven SC within half-filled band Hubbard and Hubbard-Heisenberg Hamiltonians for the superconducting CTS. We present numerical evidence for the absence of SC within the half-filled band correlated-electron Hamiltonians for any degree of frustration. We then develop a valence-bond theory of SC within which the superconducting state is reached by the destabilization of the PEC by additional pressure-induced lattice frustration that makes the spin-singlets mobile. We present limited but accurate numerical evidence for the existence of such a charge order-SC duality. Our proposed mechanism for SC is the same for CTS in which the proximate semiconducting state is antiferromagnetic instead of charge-ordered, with the only difference that SC in the former is generated via a fluctuating spin-singlet state as opposed to static PEC. In Appendix B we point out that several classes of unconventional superconductors share the same band-filling of one-quarter with the superconducting CTS. In many of these materials there are also indications of similar intertwined charge order and SC. We discuss the transferability of our valence-bond theory of SC to these systems. (C) 2018 Elsevier B.V. All rights reserved.