Anisotropic mass enhancement factors of $\bar {\Gamma }$ state on Be(0001) surface

It is controversial on the values of mass enhancement factors, $\lambda $, of Be(0001) $\bar {\Gamma }$ state. Three possible explanations are: (1) $\lambda $ is anisotropic along the Fermi circle; (2) method-based difference for extracting $\lambda $; (3) failure of theoretical model for capturing EPC features. We demonstrate a systematically survey of $\lambda $ along the Fermi circle of Be(0001) $\bar {\Gamma }$ state. By adopting different methods to extract $\lambda $, the possibility of method-based inconsistency was ruled out. The trend of the anisotropic $\lambda $ is clear and is confirmed by theoretical calculations, though the values are inconsistent with experiment. With model data simulation, we are confident about the extracted $\lambda $ while we have noisy data. The possible explanation is that the DFT-LDA calculation can not catch the features of EPC on Be(0001) $\bar {\Gamma }$ state correctly. This work is financially supported by National Science Foundation (grants NSF-DMR-0451163).