Extended Data Fig. 3: Electronic structure of finite nontrivial 7/9-AGNR superlattice.
a, Fully relaxed finite (8-supercell) 7/9-AGNR superlattice with end (green) and bulk (red) unit cells indicated. b, DFT-calculated projected DOS of the finite (8-supercell) 7/9-AGNR superlattice obtained from the end unit cell (green) and a bulk unit cell (red) (Gaussian broadening of 0.05 eV was used here). Three end states are seen that closely correspond to the experimental end states shown in Fig. 3b. c, DFT-calculated band structure of 7/9-AGNR showing the overall value of \({{\mathbb{Z}}}_{2}\) for occupation up to all three energy gaps around EF based on the edge structure shown in Fig. 3a. d, Chart of frontier band parity eigenvalues and corresponding \({{\mathbb{Z}}}_{2}\) invariants for electron filling up to and including a given frontier band. This superlattice end-state behaviour is different from the behaviour of a ‘straight-edge’ topologically nontrivial AGNR owing to the presence of multiple energy gaps that can accommodate topologically protected end states rather than only a single gap.
