Theory of non-Fermi liquid and pairing in electron-doped cuprates

Abstract

We apply the spin-fermion model to study the normal state and pairing instability in electron-doped cuprates near the antiferromagnetic quantum-critical point. Peculiar frequency dependencies of the normal state properties are shown to emerge from the self-consistent equations on the fermionic and bosonic self-energies, and are in agreement with experimentally observed ones. We argue that the pairing instability is in the ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ channel, as in hole-doped cuprates, but theoretical ${T}_{c}$ is much lower than in the hole-doped case. For the same hopping integrals and the interaction strength as in hole-doped materials, we obtain ${T}_{c}\ensuremath{\sim}10\phantom{\rule{0.3em}{0ex}}\mathrm{K}$ at the end point of the antiferromagnetic phase. We argue that a strong reduction of ${T}_{c}$ in electron-doped cuprates compared to hole-doped ones is due to critical role of the Fermi surface curvature for electron-doped materials. The ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$-pairing gap $\ensuremath{\Delta}(\mathbf{k},\ensuremath{\omega})$ is strongly nonmonotonic along the Fermi surface. The position of the gap maxima, however, does not coincide with the hot spots, as the nonmonotonic ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ gap persists even at doping when the hot spots merge on the Brillouin zone diagonals.