Topological quantum properties of chiral crystals

TL;DR

This paper uncovers a universal topological electronic property called Kramers-Weyl fermions in all nonmagnetic chiral crystals with spin-orbit coupling, revealing new phenomena and expanding understanding of their quantum behaviors.

Contribution

It introduces Kramers-Weyl fermions as a new class of topological quasiparticles enforced by crystal symmetry and structural chirality, relevant to many chiral materials.

Findings

Kramers-Weyl fermions appear at TRIMs in nonmagnetic chiral crystals with SOC.

All point-like nodal degeneracies in these crystals carry nontrivial Chern numbers.

Kramers-Weyl fermions enable novel phenomena like unique spin textures and chiral Fermi surfaces.

Abstract

Chiral crystals are materials whose lattice structure has a well-defined handedness due to the lack of inversion, mirror, or other roto-inversion symmetries. These crystals represent a broad, important class of quantum materials; their structural chirality has been found to allow for a wide range of phenomena in condensed matter physics, including skyrmions in chiral magnets, unconventional pairing in chiral superconductors, nonlocal transport and unique magnetoelectric effects in chiral metals, as well as enantioselective photoresponse. Nevertheless, while these phenomena have been intensely investigated, the topological electronic properties of chiral crystals have still remained largely uncharacterized. While recent theoretical advances have shown that the presence of crystalline symmetries can protect novel band crossings in 2D and 3D systems, we present a new class of Weyl fermions enforced by the absence of particular crystal symmetries. These "Kramers-Weyl" fermions are a universal topological electronic property of all nonmagnetic chiral crystals with spin-orbit coupling (SOC); they are guaranteed by lattice translation, structural chirality, and time-reversal symmetry, and unlike conventional Weyl fermions, appear at time-reversal-invariant momenta (TRIMs). We cement this finding by identifying representative chiral materials in the majority of the 65 chiral space groups in which Kramers-Weyl fermions are relevant to low-energy physics. By combining our analysis with the results of previous works, we determine that all point-like nodal degeneracies in nonmagnetic chiral crystals with relevant SOC carry nontrivial Chern numbers. We further show that, beyond the previous phenomena allowed by structural chirality, Kramers-Weyl fermions enable unusual phenomena, such as a novel electron spin texture, chiral bulk Fermi surfaces over large energy windows.