Solving the phase problem of diffraction: x-ray standing wave imaging on bismuthene/SiC(0001)

Abstract For establishing a fundamental understanding of the emerging properties of two-dimensional (2D) materials, a reliable determination of the crystallographic structure is essential, as we demonstrate in this work for the specific case of the quantum spin Hall insulator bismuthene. Diffraction-based methods are widely used for structure determination, however, they suffer from a fundamental shortcoming, the phase retrieval problem, that is the inability to directly measure the phase of scattered waves. The normal incidence x-ray standing wave (NIXSW) technique circumvents this problem by introducing a Bragg-generated x-ray standing wave field throughout the sample, relative to which any atomic species can be localized. In essence, a single NIXSW measurement captures the complex scattering factor (amplitude and phase) corresponding to one single Bragg reflection. Collecting data for multiple reflections enables a three-dimensional reconstruction of the scattering density as the Fourier sum of all measured scattering factors. Here, we utilize this technique to reveal the mechanism of a reversible switching process that has been reported for a 2D Bi layer recently (Tilgner et al 2025 Nat. Commun. 16 , 6171). In this prominent example, the Bi layer is confined between a 4H-SiC substrate and an epitaxial graphene layer, and can be reversibly switched between an electronically inactive precursor state and the bismuthene state. In our NIXSW imaging experiment, we clearly identify the change of the adsorption site of the Bi atoms, caused by H-saturation of one out of three Si dangling bonds per unit cell, as the key feature leading to the formation of the characteristic band structure of the 2D bismuthene honeycomb.