Spin-free quantum chemistry. XXVI. The Ising,small-bipolaron theory of cuprate superconductivity

The Ising, small-bipolaron (ISB ) theory is a strong-coupling theory of cuprate superconductivity which is based on the negative-U, Hubbard Hamiltonian. Its ground state is composed of (small) bipolarons and (small-bipolaron) holes with a vibronically induced, bipolaron-hole exchange interaction, J_BH, between them. The energy gap, Δ(0), is taken to be equal to the dissociation energy of a small bipolaron and which, since it is defined spectroscopically, is not an order parameter. The application of the Ising mean-field theory to the highly degenerate ground-state yields a second-order phase change with kT_C/2 = J_BH and a real order parameter, Ω(T), which is valid over the entire temperature range from zero to T_C. Near T_C, the Ising free-energy functional takes the same form as does the Landau. In the presence of an electromagnetic field, the Ising functional is a generalization of the Ginzburg-Landau functional which employs a complex order parameter and which is invariant under the electromagnetic gauge transformation. The breaking of the gauge invariance yields the London theory of superconductivity. © 1996 John Wiley & Sons, Inc.