Spin Dimer State Model andSpin-Phonon Coupling Model of Superconductivity

A mechanism of superconductivity coming from the doping of mobile fermions into the spin dimerized insulator such as spin Peierls state, valence bond glass, Heisenberg spins with next nearest neighbor exchange coupling and the Haldane gap state is discussed. The doping of fermions with narrow band into a Mott insulator with a spin gap results in the superconducting long range order in two- and three-dimensions, while results in the power law divergence of the pairing susceptibility with Tomonaga-Luttinger liquid character of charge in one-dimension. An example of numerical calculation in one-dimension is shown. The possible relevance of this mechanism to high-temperature superconductivity, where dynamical coupling of lattice distortion to spin may play a crucial role, is discussed. A relevant model Hamiltonian with spin-phonon coupling and dynamical spin-Peierls fluctuation is proposed.