  Nanostructures based on buried interfaces and heterostructures are at the
heart of modern semiconductor electronics as well as future devices utilizing
spintronics, multiferroics, topological effects and other novel operational
principles. Knowledge of electronic structure of these systems resolved in
electron momentum k delivers unprecedented insights into their physics. Here,
we explore 2D electron gas formed in GaN/AlGaN high-electron-mobility
transistor (HEMT) heterostructures with an ultrathin barrier layer, key
elements in current high-frequency and high-power electronics. Its electronic
structure is accessed with angle-resolved photoelectron spectroscopy whose
probing depth is pushed to a few nm using soft-X-ray synchrotron radiation. The
experiment yields direct k-space images of the electronic structure
fundamentals of this system: the Fermi surface, band dispersions and occupancy,
and the Fourier composition of wavefunctions encoded in the k-dependent
photoemission intensity. We discover significant planar anisotropy of the
electron Fermi surface and effective mass connected with relaxation of the
interfacial atomic positions, which translates into non-linear (high-field)
transport properties of the GaN/AlGaN heterostructures as an anisotropy of the
saturation drift velocity of the 2D electrons.
