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 +-0.4~0.8A, 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 0.6A. 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.