First-principles calculation of the superconducting gap function due to electron-electron interaction for YBa2Cu

Abstract

We argue that because of the anisotropic nature of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{x}}$, one-dimensional-type charge- and spin-density fluctuations produce an effective attraction that overcomes the electron-electron Coulomb repulsion, but only at large distances. This effective attraction is further enhanced by band-structure effects such that a substantial superconducting transition temperature can be obtained. Without making any assumption of the symmetry of the gap function, we solve the Bardeen-Cooper-Schrieffer (BCS) superconducting gap equation for the six bands closest to the Fermi level. A highly anisotropic gap function with a maximum of about 0.11 eV is found. From the linearized gap equation, a transition temperature of about 0.035 eV is obtained. This is about one-quarter the maximum of the gap function, consistent with the experimental ratio of the transition temperature to the gap determined from tunneling, infrared, and nuclear quadrupole resonance measurements. The important participants to the superconducting pair come from electrons close to planar copper [Cu(2)] and chain oxygen [O(1) and O(4)] sites, consistent with recent quadrupole resonance measurements. Our calculation produces a coherence length of the order of 30 A\r{} in the xy direction, the same order of magnitude as the experimental result and considerably smaller than the conventional magnitude of ordinary BCS materials. Similar calculations for ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{6.5}$ where periodic O vacancies are introduced along the one-dimensional Cu-O chains shows that the transition temperature is reduced by half.