Pressure variation of the valence band width in Ge: A self-consistent GW study

Analyzing x-ray emission spectra (XES) of germanium under pressure Struzhkin [Phys. Rev. Lett. 96, 137402 (2006)] found that the valence band width of diamond Ge does not vary with pressure. This contradicts the usual experience and also what is predicted by density-functional calculations. In the present work we report results of quasiparticle self-consistent GW (QSGW) band calculations for diamond- as well as beta-tin-type Ge under pressure. For both phases we find that the band width increases with pressure. For beta-tin Ge this agrees with experiment and density-functional theory, but for diamond Ge neither the local density approximation nor the QSGW calculations agree with the conclusions drawn from the XES data.