Topological Chiral Semimetal: Theory and Experiments*

We have shown that Kramers-Weyl fermions are a universal topological electronic property of all non-magnetic chiral crystals with spin-orbit coupling and are guaranteed by structural chirality, lattice translation, and time-reversal symmetry. We determined that all point-like nodal degeneracies in non-magnetic chiral crystals with relevant spin-orbit coupling carry non-trivial Chern numbers. Kramers–Weyl materials can exhibit a monopole-like electron spin texture and topologically non-trivial bulk Fermi surfaces over an unusually large energy window [G. Chang et al. Nature Materials 17, 978-985 (2018)]. Among all the materials, we predicted the RhSi family to exhibit the ideal topological band structures, displaying the largest possible momentum separation of compensative chiral fermions, the largest proposed topologically nontrivial energy window, and the longest possible Fermi arcs on its surface [G. Chang et al. PRL 119, 206401 (2017)]. We present the theory of exotic nonlinear optical responses of topological chiral crystals, including quantized photogalvanic effect in RhSi [G. Chang et al. PRL 119, 206401 (2017)] and robust photocurrents from Fermi arc surface states [G. Chang et al. PRL 124, 166404 (2020)]. We also discuss the experimental discovery of the RhSi family as topological chiral crystals [D. S. Sanchez et al. Nature 567, 500-505 (2019) & T. A. Cochran et al. arXiv:2004.11365 (2020)] and additional experiments that our discovery has enabled. (This work is in collaboration with D. S. Sanchez, I. Belopolski, T. A. Cochran, B. J. Wieder, F. Schindler, J. Yin, S. S. Zhang, S. Huang, B. Singh, T. Chang, A. Bansil, T. Neupert, S.-Y. Xu, H. Lin, and M. Zahid Hasan)