D9spin-polaron theory of high-Tcsuperconductivity

Abstract

The results of further studies of a ${\mathit{d}}^{9}$ spin-polaron model of high-${\mathit{T}}_{\mathit{c}}$ superconductivity are reported. Calculations of their formation energies suggest that spin polarons involving the Cu ${\mathit{d}}^{9}$ configuration and O 2p\ensuremath{\sigma} orbitals in the ${\mathrm{CuO}}_{2}$ planes should form readily in the high-${\mathit{T}}_{\mathit{c}}$ superconductors. Estimates of their radii and effective masses indicate that they are small spin polarons with masses \ensuremath{\sim} four times the band effective mass. Formation of spin polarons destroys the long-range antiferromagnetic (AF) ordering but repair of the AF order locally provides a pairing mechanism. Parametrized AF band calculations for a ${\mathrm{CuO}}_{2}$ plane show how a Mott-Hubbard (MH) gap opens as a consequence of an electron repulsion energy U at the Cu sites. The parameters are chosen to give agreement with the measured density of states, the magnetic moment per Cu site, and other data. Variation of the hole concentration by Sr doping in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ and O depletion in ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{x}}$ moves the Fermi level relative to the MH band edge. Approximate expressions for the gap and ${\mathit{T}}_{\mathit{c}}$ within the framework of a Cooper-pairing approach are derived and then solved using information from the band calculations. The proximity of the Fermi level to the MH band edge and the interplay of O 2p\ensuremath{\sigma} and 2p\ensuremath{\pi} bands and/or localization effects can provide good fits to the variations of ${\mathit{T}}_{\mathit{c}}$ with x in ${\mathrm{La}}_{2\mathrm{\ensuremath{-}}\mathit{x}}$${\mathrm{Sr}}_{\mathit{x}}$${\mathrm{CuO}}_{4}$ and ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathit{x}}$. The in-plane gap is either s- or d-like but anisotropic in either case. A discussion of various aspects and implications of the model is given.