Band theoretical approaches to topological physics in strongly-correlatedf-electron Kondo systems

First-principles band structure theory on the basis of the density functional theory (DFT) plays an essential role in the investigation of topological properties of weakly-correlated systems. DFT band structures show clear bulk band crossings for Weyl and Dirac semimetals, and surface band crossings for topological insulators and topological-crystalline insulators. In contrast, for strongly-correlatedf-electron systems, their topological properties are relatively less explored because the simple DFT does not work properly in describing the electronic structures of strongly-correlatedfelectrons. In this perspective, we examine the band theoretical approaches to topological properties of strongly-correlatedf-electron Kondo systems. We recapitulate current status of understanding of electronic structures and topological properties of strongly-correlated 4f-electron systems, such as Ce, SmB₆, and g-SmS, and also a 5f-electron system PuB₄, the electronic structures of which were investigated by the DFT combined with the dynamical mean-field theory (DFT + DMFT). Finally, we provide future directions and perspectives of improving theoretical band approaches to search for new topologicalf-electron systems, as an outlook.