The influence of exact exchange corrections in van der Waals layered narrow bandgap black phosphorus

We study the electronic structure of black phosphorus by combining state-of-the-art density functional theory, multiple scattering calculations and electron energy loss spectroscopy. The hybrid functionals HSE03 and PBE0 are tested to investigate whether they give an improved description compared to the more traditional PZ-LDA and PBE-GGA functionals. These calculations are compared with investigations of the conduction band using electron energy loss spectroscopy and calculations based on the real-space multiple scattering approach, and previous determinations of the bandgap. The hybrid functional HSE03 gives an improved correspondence with these experiments. Comparisons of the calculated valence band with previous XPS studies yield acceptable agreement for the traditional functionals, while the results from the hybrid functionals are less satisfactory, since the hybrid functionals overestimate the valence band width significantly.