Band theoretical approaches to topological physics in strongly-correlated f -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-correlated f -electron systems, their topological properties are relatively less explored because the simple DFT does not work properly in describing the electronic structures of strongly-correlated f electrons. In this perspective, we examine the band theoretical approaches to topological properties of strongly-correlated f -electron Kondo systems. We recapitulate current status of understanding of electronic structures and topological properties of strongly-correlated 4 f -electron systems, such as Ce, SmB 6 , and g-SmS, and also a 5 f -electron system PuB 4 , 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 topological f -electron systems, as an outlook.