Abstract :
A 4-site 4-electron model is extended to a square planar CuO2 sheet. The degeneracy at the Fermi level can be split in different ways and this results in a charge density wave ground state, with alternating charges on the metal sites, or an anti-ferromagnetic ground state with spin correlation. If these two states are nearly equal in energy, a magnetic ground state may appear in a perpendicular magnetic field, with persistent currents in the ground state and with paired spins. The tight-binding model is used for square planar systems with L loops and (2L)2 sites. The 2L-fold degenerate eigenvalue x=0, consistent with the Van Hove singularity, has exact eigenvector solutions which can be used as generators for other possible solutions. In the magnetic state persistent currents exist in the ground state of the hole-doped infinite system. A novel explanation is given for the `extended saddle point singularityʹ of the energy bands below Tc. Some other properties of type II superconductors may also be explained, such as the d-wave symmetry of the pair wave function.
