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

We present a study of the effects of simultaneous charge and spin frustration on the two-dimensional strongly correlated quarter-filled band on an anisotropic triangular lattice. Our conclusions are based on exact diagonalization studies that include electron-electron interactions as well as adiabatic electron-phonon coupling terms treated self-consistently. The broken-symmetry states that dominate in the weakly frustrated region near the rectangular lattice limit are the well known antiferromagnetic state with in-phase lattice dimerization along one direction and the Wigner crystal state with the checkerboard charge order. For moderate to strong frustration, however, the dominant phase is a novel spin-singlet paired-electron crystal (PEC), consisting of pairs of charge-rich sites separated by pairs of charge-poor sites. The PEC, with coexisting charge order and spin gap in two dimensions, is the quarter-filled band equivalent of the valence bond solid (VBS) that can appear in the frustrated half-filled band within antiferromagnetic spin Hamiltonians. We discuss the phase diagram as a function of onsite and intersite Coulomb interactions as well as electron-phonon coupling strength. We speculate that the spin-bonded pairs of the PEC can become mobile for even stronger frustration, giving rise to a paired-electron liquid. We discuss the implications of the PEC concept for understanding several classes of quarter-filled band materials that display unconventional superconductivity, focusing, in particular, on organic charge transfer solids. Our work points out the need to go beyond quantum spin liquid concepts for highly frustrated organic charge-transfer solids such as κ-(BEDT-TTF)₂Cu ₂(CN)₃ and EtMe₃Sb[Pd(dmit)₂] ₂, which we believe show frustration-induced charge disproportionation at low temperatures. We discuss possible application to layered cobaltates and quarter-filled band spinels.