On the use of Monkhorst–Pack scheme to evaluate superconductivity and the issue of umklapp electron–phonon interactions

Abstract

The Monkhorst–Pack scheme is a method to save time in the days of slow computers. It excludes umklapp phonons with significant consequences. Its widespread application to evaluate superconductivity arises from the desire to reduce phonon contributions to solve a historical difficulty of the BCS theory. An alternative method turns out to be more accurate in Pb and Pd.