Electronic structure of La 1.85 Sr 0.15 CuO 4 : Characterization of a Fermi-level band crossing
We present the results of a Hubbard model for optimally doped ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}.$ This model uses parameters derived from Becke-Lee-Yang-Parr calculations on the cluster ${\mathrm{CuO}}_{6}.$ It explicitly includes the Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ and ${d}_{{z}^{2}}$ orbitals, the O ${p}_{\ensuremath{\sigma}}$ orbitals, and the apical O ${p}_{z}$ orbitals. We find that when the mean-field equation is appropriately modified to include a self-interaction correction, a crossing of two bands is observed in the vicinity of the Fermi level for the optimally doped superconductor. This crossing rigorously occurs along the $(0,0)\ensuremath{-}(\ensuremath{\pi}/a,\ensuremath{\pi}/a)$ direction of the two-dimensional (2D) Brillouin zone. The crossing arises due to the overlap of a broad ``${B}_{1g}$'' band dominated by Cu ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ character and a narrower ``${A}_{1g}$'' band dominated by Cu ${d}_{{z}^{2}}$ character. We conclude that optimal doping of ${\mathrm{La}}_{2\ensuremath{-}x}{\mathrm{Sr}}_{x}{\mathrm{CuO}}_{4}$ and related materials is achieved when the Fermi level coincides with this crossing. At this point, formation of Cooper pairs between the two bands (i.e., interband pairing or IBP) leads to superconductivity. We further extend our conclusions to ${\mathrm{YBa}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6+\mathrm{\ensuremath{\delta}}}$ and offer a simple explanation for the seemingly complex behavior of ${T}_{c}$ as a function of doping in this material. This behavior can be understood on the basis of multiple band crossings predicted from geometric considerations.