Direct imaging of valence orbitals using hard x-ray photoelectron spectroscopy

It was hypothesized already more than 40 years ago that photoelectron spectroscopy should in principle be able to image atomic orbitals. If this can be made to work for orbitals in crystalline solids, one would have literally a different view on the electronic structure of a wide range of quantum materials. Here, we demonstrate how hard x-ray photoelectron spectroscopy can make direct images of the orbitals making up the band structure of our model system, ReO_{3}. The images are energy specific and enable us to unveil the role of each of those orbitals for the chemical bonding and the Fermi surface topology. The orbital image information is complementary to that from angle-resolved photoemission and thus completes the determination of the electronic structure of materials.