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

TL;DR

This paper investigates how an electronic topological transition (ETT) influences superconducting properties in two-dimensional materials, revealing nonmonotonic behavior of key parameters and providing analytical insights aligned with experimental observations.

Contribution

It presents analytical expressions for the maxima of superconducting gap, Tc, and impurity scattering near ETT in 2D superconductors, extending understanding beyond 3D cases.

Findings

Superconducting gap, Tc, and impurity scattering rate show nonmonotonic behavior near ETT.

Analytical formulas for maxima of these parameters are derived for s-wave and d-wave symmetries.

Ginzburg-Landau stiffness remains finite at ETT, contrary to expectations, affecting fluctuation effects.

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 Tc^max 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 eta. 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 eta different from 0, as a result of an integration over the whole Fermi surface.