Fig. 2: Eigenfrequencies and edge states of the supercells.

a–c The eigenfrequency spectra and the edge states of the x-PBC/y-OBC supercells with armchair boundary configurations. The left panels are the supercell configurations. The middle panels are the 3D eigenfrequency spectra. The right panels are the field patterns of select eigenstates. The color of each node denotes the value of \({\mathrm{ln}}\left|U/{U}_{\max }\right|\), where \(U\) is the voltage, and \({U}_{\max }\) is the maximum voltage among all nodes. The Roman numerals correspond to specific frequency points in the 3D spectra. Patterns (i) and (ii) are chiral edge states, whereas patterns (iii) and (iv) are non-chiral edge states. d, e The eigenfrequency spectra and the edge states of the x-OBC/y-PBC supercells with zigzag boundary configurations. The upper, middle and lower panels are the supercell configurations, the 3D eigenfrequency spectra and selected eigenstates, respectively.