On the dependence of the superconducting gap on the wave vector in Pr$_{0.89}$LaCe$_{0.11}$CuO$_{4}$

The solutions of the Bardeen–Cooper–Schrieffer equation are found within the model of the lower Hubbard subband taking into account three-site correlations and the superexchange, Coulomb, phonon, and spinfluctuation mechanisms of quasiparticle pairing. The Pr$_{0.89}$LaCe$_{0.11}$CuO$_{4}$ compound is considered as an example. The dependence of the superconducting gap on the wave vector along the Fermi contour is approximated by the expression $\Delta_{\varphi} = \Delta_{0} \left(B \cos(2\varphi) + (1 - B) \cos(6\varphi)\right)$ where the angle $\varphi$ is measured from the edge of the Brillouin zone. The calculated parameters $\Delta_0$ and $B$ correspond to the experimental data. The role of the phonon mechanism is relatively small. The competition of other specified mechanisms in the formation of $\Delta_0$ is quite strong. The effect of their interference is important and is different in different parts of the Fermi surface. The main contribution to the formation of the component proportional to $\cos(6\varphi)$ (the highest harmonic of the gap) is due to the spin-fluctuation and Coulomb interactions. It is numerically and analytically proved that the role of three-site correlations is reduced to weakening the superexchange mechanism.