Topological Quantum Properties of Chiral Crystals*

Chiral crystals are materials whose lattice structure with a well-defined handedness due to the lack of inversion, mirror, or other roto-inversion symmetries, which represent a broad, important class of quantum materials. Yet, the topological properties of chiral crystals have still remained largely uncharacterized. Here, we show that Kramers-Weyl fermions are a universal topological electronic property of chiral crystals with spin-orbit coupling (SOC). Unlike conventional Weyl fermions, they appear at time-reversal-invariant momenta. By combining our analysis with the results of previous works, we further determine that all point-like nodal degeneracies in nonmagnetic chiral crystals with relevant SOC carry nontrivial Chern numbers. Using this theory, we identify representative chiral materials in 33 of the 65 chiral space groups in which topological chiral fermions are relevant to low-energy physics. Among all the materials, RhSi family exhibit the ideal topological band structures with longest Fermi arcs and nontrivial energy windows.
[1] Nat. Mater. 17, 978–985
[2] Phys. Rev. Lett. 119, 206401