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Theoretical calculations of Angle-Resolved PhotoEmission Spectra can achieve a very high level of accuracy, even for complex materials. In the figure, experimental measurements are compared against different theoretical predictions for bulk Cu$_2$O, a rather complicated material containing d-electrons. The levels of theory employed here are the standard Local-Density Approximation, the GW method, and the "self-consistent GW" (SCGW). In the panel a), the experimental spectrum is compared with the calculated density-of-states within the SCGW. The panel b) provides angle-resolved experimental data as a color plot in the background. The different levels of theoretical treatment, going from the simplest, LDA (grey lines), to GW (black lines) and self-consistent GW (red diamonds) show a consistent improvement when increasing the complexity of the calculations. The SCGW results show a quantitative level of accuracy (after F. Bruneval et al., Phys. Rev. Lett. 97, 267601 (2006) ).