Electronic structure of black phosphorus studied by polarized soft-x-ray emission and absorption spectroscopy

Soft-x-ray emission ($K\beta$ emission) and absorption ($K$ absorption) spectra of a black P single crystal polarized along each crystalline axis are presented for the first time. The experimental results indicate (1) the upper part of the valence band near the Fermi level is largely contributed by the $3p_z$ states, (2) the $3p_y$ orbital forms the middle to lower part of the $3p$-derived (or the first) valence band, (3) the $3p_x$ states spread over a whole range in the band, and (4) the conduction band has a clear but less drastic dependence on the nature of the constituent atomic orbitals. The emission and absorption curves were numerically calculated with the results of the band calculation of black P based on the self-consistent pseudopotential method and were compared with the experimental results. Excellent agreement has been found in the features of each spectrum, although a relative displacement of the emission and absorption spectra was observed between the experiment and the calculation. This discrepancy may be attributed to the overestimation of the $3p$-band width in the band calculation, although a many-body effect in the emission or absorption process cannot be entirely excluded.