Solving the Phase Problem of Diffraction: X-ray Standing Waves Imaging on Bismuthene/SiC(0001)

Abstract

The phase retrieval problem is a fundamental shortcoming of all diffraction-based methods, arising from the inability to measure the phase of scattered waves. The (normal incidence) X-ray standing wave (NIXSW) technique circumvents this issue by introducing a (Bragg-generated) X-ray standing wave field throughout the sample, relative to which any atomic species can be localized by probing its fluorescence or photoelectron yield. In essence, in a single measurement the complex scattering factor (i.e., its amplitude \textit{and} phase) corresponding to the used Bragg reflection is determined. Performing this for multiple Bragg reflections enables one to reconstruct the scattering density of the sample in three dimensions, straightforwardly as the Fourier sum of all measured (complex) scattering factors. Here, we utilize this technique to reveal the structural key features involved in the formation of the quantum spin Hall insulator bismuthene on silicon carbide. In this prominent example, the two-dimensional Bi layer is confined between a 4H-SiC substrate crystal and an epitaxial graphene layer. The key finding is a change in the adsorption site of the Bi atoms underneath the graphene upon hydrogenation, caused by the H-saturation of one (out of three) Si dangling bonds per unit cell. This structural change, clearly revealed by our NIXSW imaging experiment, is the key feature leading to the formation of the characteristic band structure of the 2D bismuthene honeycomb.