2D fermionic systems near a magnetic $2k_F$ instability: application to electron-doped cuprates

We study spin-mediated pairing in 2D itinerant electron systems near antiferromagnetic instability in a situation when the antiferromagnetic vector $(\pi,\pi)$ connects nodal points on the Fermi surface. This scenario is related to the electron-doped high- $T_{c}$ materials where the variation of the Fermi surface with doping drives the hot spots towards zone diagonals. We obtain fermionic self-energy at strong coupling and analyze the $d-$wave pairing problem.