Electronic Structure of B-2p State in AlB2 Single Crystal: Direct Observation ofpσ and pπ Density of States

X-ray emission (XES) and absorption (XAS) spectra near the B-$K$ edge were measured on single-crystalline AlB$_2$ compound which is an isostructural diboride of superconducting MgB$_2$. The partial density of states (PDOS) of B-2$p\sigma$ and $p\pi$ orbitals were derived from the polarization dependence of XES and XAS spectra. There are considerable amounts of PDOS near the Fermi energy in AlB$_2$ similarly to that in MgB$_2$, but there are almost no PDOS in $p\sigma$ orbitals of AlB$_2$ near the Fermi energy, i.e., a pseudo-gap in $p\sigma$ state and a broad metallic state in $p\pi$ state are observed. The present result indirectly supports scenarios that the $p\sigma$ holes play an important role in the occurrence of superconductivity in MgB$_2$. The overall features of PDOS were found to be in good agreement with the result of band calculation of AlB$_2$, but a small discrepancy in the Fermi energy is observed, which is attributed to the Al vacancy in the compounds, i.e., the estimated concentration is Al$_{0.93}$B$_2$.