Table 2 Space groups (SGs) that admit Dirac points with HOFA states derived from the QI introduced in ref. 23.

From: Strong and fragile topological Dirac semimetals with higher-order Fermi arcs

Space groups admitting dirac points with HOFA states

Point group name

Point group symbol

SG numbers

C4v

\( 4mm1^{\prime} \)

99–110

D4h

\( 4/mmm1^{\prime} \)

123–142

Oh

\( m\bar{3}m1^{\prime} \)

221–230

  1. All of these SGs have point groups that contain C4v. We obtain this list of SGs by combining the nested Jackiw–Rebbi formulation of the QI in Supplementary Note 6 with an analysis of the crystallographic rod groups in Supplementary Note 12. In all of these SGs, semimetals with Dirac points along lines with 4 mm or \( 4/m^{\prime} mm \) symmetry will exhibit intrinsic HOFA states when cut into nanorods that preserve fourfold axes and are thick compared with the in-plane lattice spacing. This list is a complete enumeration of the SGs that permit Dirac semimetals with HOFA states directly related to the QI introduced in ref. 23; alternative realizations of Dirac and Weyl semimetals with HOFA states derived from other 2D magnetic insulators with corner states are also possible (refs. 32,37 and Supplementary Note 12).
Back to article page