A Study of Carbon Substitutions in MgB_2 within the two-band Eliashberg theory

TL;DR

This study models how carbon substitution affects superconducting properties in MgB_2 using a two-band Eliashberg approach, revealing how parameters like Coulomb pseudopotential and interband scattering influence the gaps and critical temperature.

Contribution

It introduces a detailed two-band Eliashberg model incorporating first-principles data to analyze C substitution effects in MgB_2, highlighting the roles of Coulomb interactions and interband scattering.

Findings

Linear decrease of Coulomb pseudopotential with C content

Interband scattering causes gap merging at x=0.132 in single crystals

No interband scattering needed to fit polycrystal data

Abstract

We study the effects of C substitutions in MgB_2 within the two-band model in the Eliashberg formulation. We use as input the B-B stretching-mode frequency and the partial densities of states N_{sigma}(EF) and N_{pi}(EF), recently calculated for Mg(B_{1-x}C_{x})_2 at various x values from first-principles density functional methods. We then take the prefactor in the Coulomb pseudopotential matrix, mu, and the interband scattering parameter, Gamma^{sigma pi}, as the only adjustable parameters. The dependence on the C content of Tc and of the gaps (Delta_{sigma} and Delta_{pi}) recently measured in Mg(B_{1-x}C_{x})_2 single crystals indicate an almost linear decrease of mu on increasing x, with an increase in interband scattering that makes the gaps merge at x=0.132. In polycrystals, instead, where the gap merging is not observed, no interband scattering is required to fit the experimental data.