Checkerboard patterns and magnetic resonance peak in cuprate superconductors

We investigate a kind of spin-Peierls transition (SP) in high Tc superconductivity. It is found the antiferromagnetic exchange integral of SP corresponds to the magnetic resonance peak. The kind of spin-Peierls transition applied to cuprate superconductors is that without dimerization of lattice ions and with dimerization of localized hole hCu attached to the ion. Absence of the magnetic resonance peak in La–Sr–Cu–O results from the dimerized state of localized hole, hCu below Tc into tetramerized phase above Tc in SP transition without dimerization of copper-ion. The checkerboard patterns with four unit cell period originate from the SP of electronic part without ion-dimerization and from charge occupation probability of oxygen-atom around Cu.