High-chirality and multiquaternion Weyl nodes in hexagonal ReO$_3$

Abstract

The formation of two-band nodal points in gapless topological phases, referred to as conventional Weyl nodes, relies solely on translational symmetry. However, when coupled with other spatial and spatio-temporal symmetries, unconventional Weyl nodes with high degeneracy, pronounced chirality, and complementary quaternion charges can manifest. In this work, we identify ReO3 as an ideal unconventional Weyl semimetal in which rotation and screw symmetries as well as their combination with time-reversal symmetry play a crucial role. To show this, we first revisit in detail the algebraic determination of the chirality of Weyl nodes from the spinful irreducible representations of the occupied and unoccupied bands, and then combine it with the complementary C2T-symmetry-protected patch Euler class and non-Abelian frame charges that indicates the pinning of the Weyl nodes on C2T-invariant planes. Supporting our findings with first-principles calculations, we furthermore reveal very clear Fermi arc signatures of the high-chirality Weyl nodes at the Fermi level for different surface orientations. We finally investigate the effect of strain upon which the robustness of Weyl nodes clearly demonstrates their Chern (i.e. chirality conservation) and quaternionic (i.e. symmetry-plane pinning) topological nature.