Inversion of two-band superconductivity at the critical electron doping of (Mg,Al)B$_2$

TL;DR

This study investigates how Al doping affects two-band superconductivity in MgB$_2$, revealing an inversion of band dominance as the $\sigma$ band loses its superconducting gap with increased doping.

Contribution

It provides experimental evidence of the inversion of two-band superconductivity in MgB$_2$ due to Al doping, combining EELS and heat capacity measurements with theoretical predictions.

Findings

$\sigma$-band hole states disappear above 33% Al doping.

Superconductivity persists with $T_c < 7$ K up to 55% Al doping.

Inversion of band hierarchy occurs as $\sigma$ band becomes weaker than $\pi$ band.

Abstract

Electron energy-loss spectroscopy (EELS) was combined with heat capacity measurements to follow the change of superconductivity with systematic Al doping of MgB$_2$. By using x-ray diffraction and Vegard's law to assess the actual Al content in the samples, changes in behavior were found to be much more in agreement with theoretical predictions than in earlier studies. EELS data show that $\sigma$-band hole states disappear above 33% Al, approximately the composition at which the $\sigma$ band Fermi surface is predicted to lose its cylindrical shape in reciprocal space and break apart into ellipsoidal pockets. At this composition, the $\sigma$ gap obtained from the heat capacity data falls to the level of the $\pi$ gap, implying that band filling results in the loss of strong superconductivity on the $\sigma$ band. However, superconductivity is not quenched completely, but persists with $T_c < 7$ K up to about 55% Al, the Al concentration at which the entire $\sigma$ band is predicted to fall below the Fermi surface. Since, in the region $0.33 \alt x \alt 0.55$, only the $\pi$ band has appreciable density of states, it becomes the stronger of the 2 bands, thus inverting the 2-band hierarchy of MgB$_2$.