The full 3D electronic band structure of MgB2 determined by soft x-ray ARPES

MgB$_{2}$ is a prototypical multi-band multi-gap superconductor with electron-phonon coupling driving T$_{c}$ up to 40~K. Surprisingly, the experimental knowledge of the electronic band structure is rather limited. Here, we present the first results of angle-resolved photoelectron spectroscopy (ARPES) studies on high quality MgB$_{2}$ single crystals, employing photons in the soft x-ray range with variable energy. We have been able to measure the band dispersion not only in the $k_{\rm x}$-$k_{\rm y}$ plane, but also probe in detail the $k_{\rm z}$ dependence and thus, the 3D nature of the bands. Furthermore, we have found the ARPES intensities to be strongly polarization dependent and their analysis provides an excellent agreement with the orbital nature of the electronic states. The calculated electronic band structure captures very well all the features revealed in our experiment.