Fig. 5: Edge response of multi-gap non-abelian braiding.
From: Minimal non-abelian nodal braiding in ideal metamaterials
a Quotient relation that relates a nodal charge (\(Q\)) and the non-Abelian charges defined for two constant-\({k}_{x}\) loops (\({q}_{r}\) and \({q}_{l}\)). b \({k}_{x}\) evolution of the loop charge (dubbed \(q\) in general) exemplified for the case of \(t=2\). Zak phases of the three bands (from the lowest to the highest) are indicated for different \({k}_{x}\) intervals. c A summary of the correlation between the loop charge and the presence (☑) or absence (☒) of the edge states in gap-I and gap-II. d–k Experimentally measured edge spectra (color scale) for a sequence of instants, compared with the associated simulation results (white and color lines for the bulk and edge, respectively). The arrows highlight the edge projections of the band nodes (circles), between which the corresponding loop charges are specified.
