Band filling and interband scattering effects in MgB$_2$: C vs Al doping

TL;DR

This paper uses band structure calculations and Eliashberg theory to explain how electron doping from Al and C affects the superconducting transition temperature and gap behavior in MgB$_2$, resolving previous discrepancies.

Contribution

It demonstrates that band filling and interband scattering together explain the doping effects on MgB$_2$'s superconducting gaps and transition temperature.

Findings

Doping reduces $T_c$ mainly through band filling effects.

The $ ext{pi}$ gap remains nearly constant due to compensation between band filling and interband scattering.

The merging point of the gaps shifts to higher doping levels, aligning theory with experiments.

Abstract

We argue, based on band structure calculations and Eliashberg theory, that the observed decrease of $T_c$ of Al and C doped MgB$_2$ samples can be understood mainly in terms of a band filling effect due to the electron doping by Al and C. A simple scaling of the electron-phonon coupling constant $\lambda$ by the variation of the density of states as function of electron doping is sufficient to capture the experimentally observed behavior. Further, we also explain the long standing open question of the experimental observation of a nearly constant $\pi$ gap as function of doping by a compensation of the effect of band filling and interband scattering. Both effects together generate a nearly constant $\pi$ gap and shift the merging point of both gaps to higher doping concentrations, resolving the discrepancy between experiment and theoretical predictions based on interband scattering only.