Multiband superconductors close to a 3D-2D electronic topological transition

TL;DR

This paper investigates how the critical temperature and isotope effect in two-band superconductors are influenced by proximity to a 3D-2D electronic topological transition, revealing shape resonance effects.

Contribution

It provides a theoretical analysis of Tc and isotope exponent dependence near an electronic topological transition in two-band superconductors, linking shape resonance to experimental observations.

Findings

Tc enhancement near the ETT in MgB2 compounds.

Possible variation of isotope effect with chemical potential tuning.

Agreement with experimental Tc dependence on Mg content.

Abstract

Within the two-band model of superconductivity, we study the dependence of the critical temperature Tc and of the isotope exponent alpha in the proximity to an electronic topological transition (ETT). The ETT is associated with a 3D-2D crossover of the Fermi surface of one of the two bands: the sigma subband of the diborides. Our results agree with the observed dependence of Tc on Mg content in A_{1-x}Mg_xB_2 (A=Al or Sc), where an enhancement of Tc can be interpreted as due to the proximity to a "shape resonance". Moreover we have calculated a possible variation of the isotope effect on the superconducting critical temperature by tuning the chemical potential.