First-principles analysis of superconducting magnesium diboride under pressure using the Cooper pair distribution function Dcp(ω,Tc)

Abstract

The Cooper pair distribution function $D_{cp}(\omega ,T_c)$ is employed to analyze the behavior of the MgB${}_2$ superconductor under pressures ranging from 8 to 32 GPa. The results of $D_{cp}(\omega ,T_c)$ indicate that the formation of Cooper pairs in this compound is highly probable within the energy interval 0–35 meV, where significant vibrational contributions to phonon dispersion arise from both Mg and B atoms. Moreover, the parameters ${\omega }_{cp}$ and $N_{cp}$ obtained from $D_{cp}(\omega ,T_c)$ accurately replicate the pressure dependence of the superconducting critical temperature T${}_c$ observed in MgB${}_2$. This provides a possible phenomenological explanation for its highest experimentally measured T${}_c$. An electronic analysis of $D_{cp}(\omega ,T)$ function below the Fermi level reveals initial consistency with both theoretical and experimental results for the superconducting gap energy in MgB${}_2$. These findings demonstrate that $D_{cp}(\omega ,T_c)$ is a promising theoretical tool for studying conventional superconductors.