Kondo-lattice theory of anisotropic singlet superconductivity

Kondo-lattice theory for the t-J model and a phenomenological theory based on it are developed to study superconductivity in the vicinity of the Mott metal-insulator transition. Since the quenching of magnetic moments by single-site quantum spin fluctuations or the Kondo effect is reduced by the opening of a superconducting gap, spin density wave (SDW) can appear in a superconducting state and the Knight shift can deviate from the Yosida function to be small. The electron-phonon interaction, which arises from the modulation of the superexchange interaction by phonons, is crucial in the coexistence of superconductivity and SDW. It is proposed that the coexistence of superconductivity, a double-Q SDW, a double-Q lattice distortion, and a double-Q charge density wave induced by the SDW rather than the lattice distortion, is responsible for the checkerboard structure and the zero-temperature pseudo-gap observed in under-doped cuprate superconductors.