High-chirality and multiquaternion Weyl nodes in hexagonal ReO3

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 spatiotemporal symmetries, unconventional Weyl nodes with pronounced chirality, high degeneracy, and complementary quaternion charges can manifest. In this paper, we identify <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>ReO</mi> <mn>3</mn> </msub> </math> 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 doubly and triply degenerate Weyl nodes from the spinful irreducible representations of the occupied and unoccupied bands, and then combine it with the complementary <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msub> <mi>C</mi> <mn>2</mn> </msub> <mi>T</mi> </mrow> </math> -symmetry-protected patch Euler class and non-Abelian frame charges that indicate the pinning of the Weyl nodes on <math xmlns="http://www.w3.org/1998/Math/MathML"> <mrow> <msub> <mi>C</mi> <mn>2</mn> </msub> <mi>T</mi> </mrow> </math> -invariant planes. Notably, we find one of the Weyl nodes in <math xmlns="http://www.w3.org/1998/Math/MathML"> <msub> <mi>ReO</mi> <mn>3</mn> </msub> </math> as the first example of a node with multiple nontrivial quaternion charges. 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.