The prediction and discovery of new topological states of matter and their effects on the bulk properties of materials has attracted widespread attention [1,2], as they are promising candidates for future technological applications such as quantum computing, memory storage, and sensors.  While much of the research has focused on the exploration of topological states in materials without strong electronic correlations (e.g. Bi₂Se₃), these correlations open up new routes to generating novel topological states.  For example, the competing interactions among the magnetic moments of d- or f-electrons leads to magnetic frustration and often gives rise to non-collinear or non-coplanar spin structures. Mobile conduction electrons feel the effects of a large (fictitious) magnetic field when they move in the topological spin texture of these non-collinear and non-coplanar magnets, which gives rise to a large anomalous Hall effect in compounds such as Mn₃Sn [5]. Furthermore, the conducting surface state in the Kondo insulator SmB₆, produced from strong hybridization of the Sm 4f electron and conduction electron states, may be a new example of a topological state in a correlated electron material [3,4].  Actinide compounds, with their larger overlap of the f-electron orbitals with neighboring ligand orbitals, often have larger characteristic energy scales and provide fertile ground for searching for new and interesting topological materials. In this talk, I discuss our recent work on the topological properties of the PuB₄ insulator and the non-collinear antiferromagnet Mn₃Sn.

[1] M. Z. Hasan and C. Kane, Rev. Mod. Phys. 82, 3045 (2010); X.-L. Qi, and S.-C. Zhang, Rev. Mod. Phys. 83, 1057 (2011)

[2] L. Fu and C. L. Kane, Phys. Rev. B 76, 045302 (2007)

[3] D. J. Kim,  J. Xia and Z. Fisk, Nature Materials 13, 466 (2014)

[4] M. Dzero, J. Xia, V. Galitski, and P. Coleman, Annual Review of Condensed Matter Physics 7, 249 (2016)

[3] S. Nakatsuji, N. Kiyohara, and T. Higo, Nature 527, 212 (2015)