Fig. 1: Non-Abelian topological charges in four-band models.
From: Four-band non-Abelian topological insulator and its experimental realization
a Elements of the \({Q}_{16}\) group indicated by colored spheres sitting on an outstretched regular octahedron and their mutual multiplications represented by the corresponding colored arrows. For example, a red arrow \({q}_{12}\) brings a blue sphere \({q}_{23}\) to a cyan sphere \({q}_{13}\), indicating that \({q}_{23}{q}_{12}={q}_{13}\). Full multiplication tables are provided in Supplementary Tables 1 and 2. b–e Extended 2D bands corresponding to three different categories of the non-Abelian topological charges: \(\pm {q}_{{mn}}\), \({q}_{1234}\), and \(\pm 1\). White circles indicate the corresponding 1D bands. The charge \({q}_{1234}\) can be decomposed in three ways in c, which are all topologically equivalent. For charge \(-1\), we take \(-1={q}_{12}^{2}\) as an example, and the other cases can be simply obtained by changing the linear Dirac cone degeneracies in panel b to quadratic degeneracies without any position shifting.
