Antiferromagnetic fluctuations, symmetry, and shape of the gap function in the electron-doped superconductors: Functional renormalization-group analysis

Abstract

The problem of symmetry of superconducting pairing and the form of the gap function in the electron-doped superconductors is reconsidered within the temperature-cutoff functional renormalization-group approach combined with the Bethe-Salpeter equations. The momentum dependence of the order parameter for antiferromagnetic and superconducting instabilities in these compounds is analyzed. The gap function in the antiferromagnetic (particle-hole) channel has its maxima at the hot spots, or at the diagonal of the Brillouin zone in their absence. The wave function in the singlet superconducting channel is nonmonotonic in the vicinity of the $(\ensuremath{\pi},0)$ and $(0,\ensuremath{\pi})$ points, deviating therefore from the conventional $d$-wave form in striking similarity with recent experimental data. An instability in the triplet superconducting channel is much weaker than in the singlet one and has $f$-wave-like form of the gap function.