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. 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. Uniquely in the quarter-filled band, there is a very strong tendency to form nearest neighbor spin-singlets, in both one and two dimensions. 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 state and the Wigner crystal of single electrons. Further, unlike these classical broken symmetries, the PEC is characterized by a spin gap. The tendency to the PEC in two dimensions is enhanced by lattice frustration. 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 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. 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.