Superconductivity in the vicinity of a 2D electronic topological transition

We review some results concerning the superconducting properties of a 2D superconductor in the proximity to an electronic topological transition (ETT). In contrast to the 3D case, we find that the superconducting gap at T = 0 is characterized by a nonmonotonic behavior, with maxima occurring close to the ETT, both for s- and for d-wave pairing. Such a result is in good qualitative agreement with the phenomenological trend recently observed for T-c(max) as a function of the hopping ratio t'/t for several cuprate compounds. We also derive a nonmonotonic dependence of the quasipaxticle inverse lifetime due to impurity scattering. We further analyze the effect of an ETT on the Ginzburg-Landau stiffness eta, for which we recover an expression analogous to the case of an isotropic dispersion relation.