Infinite-range Heisenberg model and high-temperature superconductivity

A strongly coupled variational wave function, the doublet spin-projected Néel state (DSPN), is proposed for oxygen holes in three-band models of high-temperature superconductors. This wave function has the three-spin system of the oxygen hole plus the two neighboring copper atoms coupled in a spin-1/2 doublet. The copper spins in the neighborhood of a hole are in an eigenstate of the infinite-range Heisenberg antiferromagnet (SPN state). The doublet three-spin magnetic polaron or hopping polaron (HP) is stabilized by the hopping terms ${\mathit{t}}_{\mathrm{\sigma }}$ and ${\mathit{t}}_{\mathrm{\tau }}$, rather than by the copper-oxygen antiferromagnetic coupling ${\mathit{J}}_{\mathrm{pd}}$. Although, the HP has a large projection onto the Emery (${\mathit{D}}_{\mathit{g}}$) polaron, a non-negligible amount of doublet-u (${\mathit{D}}_{\mathit{u}}$) character is required for optimal hopping stabilization. This is due to ${\mathit{J}}_{\mathit{d}\mathit{d}}$, the copper-copper antiferromagnetic coupling. For the copper spins near an oxygen hole, the copper-copper antiferromagnetic coupling can be considered to be almost infinite ranged, since the copper-spin-correlation length in the superconducting phase (0.06–0.25 holes per in-plane copper) is approximately equal to the mean separation of the holes (between 2 and 4 lattice spacings). The general DSPN wave function is constructed for the motion of a single quasiparticle in an antiferromagnetic background. The SPN state allows simple calculations of various couplings of the oxygen hole with the copper spins. The energy minimum is found at symmetry (π/2,π/2) and the bandwidth scales with ${\mathit{J}}_{\mathit{d}\mathit{d}}$. These results are in agreement with exact computations on a lattice. The coupling of the quasiparticles leads to an attraction of holes and its magnitude is estimated.