Abstract
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 [Formula: see text] as a function of the hopping ratio t′/t for several cuprate compounds. We also derive a nonmonotonic dependence of the quasiparticle inverse lifetime due to impurity scattering. We further analyze the effect of an ETT on the Ginzburg-Landau stiffness η, for which we recover an expression analogous to the case of an isotropic dispersion relation.
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