Knowledge Bank

To understand the superconductivity in $La2-xSrxCu1O4,Y1Ba2Cu2O7$, and $TI2Ba2CaCu2O6$, we carried out quantum chemical (generalized valence bond) calculations on various clusters to obtain information about the electronic states of the oxidized systems and about the magnetic interactions. In addition, on these we used the recently developed valence-bond band theory to calculate the energy bands for these systems. These results indicate that (i) all copper sites have a $CuII(d9)$ oxidation state with one unpaired spin that is coupled antiferromagnetically to the spins of adjacent $CuII$ sites; (ii) oxidation beyond the cupric $(CuII)$ state leads not to $CuIII$ but rather to oxidized oxygen atoms, with an oxygen p hole bridging two $CuII$ sites; (iii) the hopping of these oxygen p holes (in CuO sheets) from site to site is responsible for the conductivity in these systems; and (iv) the oxygen p hole at these oxidized sites is ferromagnetically coupled to the adjacent $CuII$ d electrons despite the fact that this is opposed by the direct dd exchange. Using these ideas, we derived the magnon pairing mechanism to explain the high-temperature superconductivity of all three systems. Critical features include (i) a one- or two-dimensional lattice of linear Cu-O-Cu bonds that contribute to large antiferromagnetic (superexchange) coupling of the $CuII(d9)$ orbitals; (ii) holes in the oxygen p bands [rather than $CuIII(d8)$] leading to high mobility hole conduction; and (iii) strong ferromagnetic coupling between oxygen p holes and adjacent $CuII(d9)$ electrons. The ferromagnetic coupling of the conduction electrons with copper d spins induces the attractive interaction responsible for the superconductivity. The disordered Heisenberg lattice of antiferromagnetically coupled copper d spins serves a role analogous to the phonons in a conventional system. This theory has been used to solve self-consistently for the k-dependent energy gap as a function of temperature. In addition, we have calculated the critical magnetic fields, the specific heat, and the tunneling as a function of temperature. This model leads to suggestions concerning modifications of current materials to improve Tc and suggests limits to the Tc for current materials.