Effects of an electronic topological transition for anisotropic low-dimensional superconductors

Abstract

We study the superconducting properties of a two-dimensional 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, the critical temperature Tc, and the impurity scattering rate are characterized by a nonmonotonic behavior, with maxima occurring close to the ETT. We derive analytical expressions for the value of such maxima both in the s-wave and in the d-wave case. Such expressions are in good qualitative agreement with the phenomenological trend recently observed for T max c as a function of the hopping ratio t ′ /t across several cuprate compounds. We further analyze the effect of an ETT on the Ginzburg-Landau stiffness η. Instead of vanishing at the ETT, as could be expected, thus giving rise to an increase of the fluctuation effects, in the case of momentum-independent electron-electron interaction, we find η = 0, as a result of an integration over the whole Fermi surface.

Effects of proximity to an electronic topological transition on normal-state transport properties of thehigh−Tcsuperconductors

“…Given that a nonzero value of the hopping ratio r can be associated with structural distortions in the ab plane of the cuprates, 30 one may conclude that in-plane anisotropy enhances the fluctuation effects associated to a nonzero value of Im ␥. Moreover, on the basis of the direct correlation existing between T c,max and the hopping ratio r, 33,29 it follows that the heights of the peaks in Im ␥ around the ETT increase with increasing T c,max across different classes of cuprates. Such a result is in agreement with the data listed in Table I for the excess Hall parameter ␤ϰIm ␥.…”

Pseudogap from ARPES experiment: Three gaps in cuprates and topological superconductivity (Review Article)

“…The role of Lifshitz transition can be twofold here: shaping the spectrum of magnetic fluctuations [315] and formation of critically slow quasiparticles [316]. Earlier, an enhancement of superconductivity due to proximity to Lifshitz transition has been discussed in connection to the (π, 0) saddle point [317] (see also [318] and references therein), but the main objection against the relevance of this scenario for the cuprates was that for optimal doping the saddle point is essentially below the Fermi level.…”

Multiband Superconductors Close to a 3D–2D Electronic Topological Transition

“…[13,14] for recent reviews). The proximity to an essentially 2D ETT in the cuprates has been recently connected with the non-monotonic dependence of T c on doping [15], with the universal dependence of T c on the in-plane hopping ratio [15,16], as well as with the anomalous enhancement of the effect of superconducting fluctuations on several transport properties above T c [17].…”