We use dynamical low-energy electron diffraction (LEED) to determine the surface structure of $\alpha -{\mathrm{Al}}_2{\mathrm{O}}_3\mathrm{}\left(0001\right).$ Sapphire surfaces are prepared in three different ways, and the diffraction results are analyzed using an exhaustive search of possible models. For all sample processing conditions, the clearly favored structure has a single Al layer termination and a large first interlayer contraction. In addition, we find that the aluminum atoms at the surface have unusually large vibrational amplitudes at room temperature, suggestive of an anharmonic vibrational mode.

The bulk band structure of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ has been determined by angle-resolved photoemission spectroscopy and compared to first-principles calculations. We have performed calculations using the local density approximation (LDA) of density functional theory and the one-shot $GW$ approximation within the all-electron full-potential linearized augmented-plane-wave (FLAPW) formalism, fully taking into account spin-orbit coupling. Quasiparticle effects produce significant changes in the band structure of ${\mathrm{Bi}}_2{\mathrm{Te}}_3$ when compared to LDA. Experimental and calculated results are compared in the spectral regions where distinct differences between the LDA and $GW$ results are present. Overall a superior agreement with $GW$ is found, highlighting the importance of many-body effects in the band structure of this family of topological insulators.

The surface structure of the prototypical topological insulator Bi${}_{2}$Se${}_{3}$ is determined by low-energy electron diffraction and surface x-ray diffraction at room temperature. Both approaches show that the crystal is terminated by an intact quintuple layer. Specifically, an alternative termination by a bismuth bilayer is ruled out. Surface relaxations obtained by both techniques are in good agreement with each other and found to be small. This includes the relaxation of the van der Waals gap between the first two quintuple layers.

The structural properties of graphene/Ni(111) are investigated by a combination of low-energy electron diffraction (LEED), x-ray photoelectron spectroscopy (XPS), angle-scanned photoelectron diffraction (PED), and first-principles calculations. XPS data indicate that graphene interacts strongly with the topmost Ni layer. Diffraction data show that graphene is deposited commensurably with the underlying Ni surface atoms. Twelve different graphene preparations were analyzed by LEED and one by PED. Considering the relative position between the carbon and Ni atoms, five experimental sets indicate a top-fcc structure, three show a bridge-top structure, and four have a mixed structure. The analysis of the PED experiment suggests the top-fcc termination. Our first-principles calculations show that the total energies of the top-fcc and bridge-top structures are nearly degenerate, which corroborates the observed bistability of those phases. Moreover, by comparing the structural parameters obtained by the three methods (LEED, PED, and ab initio calculations), excellent agreement is achieved.