Plasmon effect on the Coulomb pseudopotential ${\mu }^{\ast }$ in the McMillan equation

Abstract

We examine the Coulomb pseudopotential ${\mu }^{\ast }$ in the McMillan equation applying to the superconductivity of heavily doped semiconductors. Systematic calculation using the first-principles calculation suggests that ${\mu }^{\ast }$ should be considered as a variable quantity depending on carrier density $n$ in semiconductors, although it is usually considered as a constant about 0.1. To clarify $n-$dependence of ${\mu }^{\ast }$, we solve the McMillan equation inversely for ${\mu }^{\ast }$ by combining the result of the first-principles calculation and that of experiments. It indicates that ${\mu }^{\ast }$ decreases with $n$ and becomes negative under $n\sim 5\times 10^{-21}[\mathrm{c}{\mathrm{m}}^{-3}]$. This reduction is explained by the effect of plasmon which may play an important role in the superconductivity of low carrier systems such as heavily doped semiconductors.

5 pages, 2 figures