Perspective: imaging atomic step geometry to determine surface terminations of kagome materials and beyond

Here we review scanning tunneling microscopy research on the surface determination for various types of kagome materials, including 11-type (CoSn, FeSn, FeGe), 32-type (Fe₃Sn₂), 13-type (Mn₃Sn), 135-type (AV₃Sb₅, A = K, Rb, Cs), 166-type (TbMn₆Sn₆, YMn₆Sn₆ and ScV₆Sn₆), and 322-type (Co₃Sn₂S₂ and Ni₃In₂Se₂). We first demonstrate that the measured step height between different surfaces typically deviates from the expected value of ±0.4 ∼0.8Å, which is owing to the tunneling convolution effect with electronic states and becomes a serious issue for Co₃Sn₂S₂ where the expected Sn-S interlayer distance is 0.6Å. Hence, we put forward a general methodology for surface determination as atomic step geometry imaging, which is fundamental but also experimentally challenging to locate the step and to image with atomic precision. We discuss how this method can be used to resolve the surface termination puzzle in Co₃Sn₂S₂. This method provides a natural explanation for the existence of adatoms and vacancies, and beyond using unknown impurity states, we propose and use designer layer-selective substitutional chemical markers to confirm the validity of this method. Finally, we apply this method to determine the surface of a new kagome material Ni₃In₂Se₂, as a cousin of Co₃Sn₂S₂, and we image the underlying kagome geometry on the determined Se surface above the kagome layer, which directly visualizes the p-d hybridization physics. We emphasize that this general method does not rely on theory, but the determined surface identity can provide guidelines for first-principles calculations with adjustable parameters on the surface-dependent local density of states and quasi-particle interference patterns.