Fig. 5: The effective band structure of graphene quasicrystal.

a Brillouin zones of the two layers. b, c The first two strongest scattering paths for \({K}^{^{\prime} }\) (\({K}^{^{\prime} }\to {\widetilde{K}}_{1}\) and \({K}^{^{\prime} }\to {\widetilde{K}}_{2}\)). d The effective band structure of graphene quasicrystal obtained by unfolding the band structure of 15/26 approximant. The insets at the bottom left and right corners show the gaps at \(M\) and \(\widetilde{M}\) clearly. e Fermi surfaces around \(K\), \({K}_{1}\), \({K}_{2}\), \(\widetilde{K}\), \({\widetilde{K}}_{1}\), and \({\widetilde{K}}_{2}\) above Fermi energy by 35 meV. f Effective band structures around \(K\), \({K}_{1}\), \({K}_{2}\), \(\widetilde{K}\), \({\widetilde{K}}_{1}\), and \({\widetilde{K}}_{2}\) along four directions. The larger spectral function is denoted by larger black dot in (d, f) and lighter color in (e), respectively. The spectral functions around \({K}_{1}\)/\({\widetilde{K}}_{1}\) and \({K}_{2}\)/\({\widetilde{K}}_{2}\) are multiplied by 300 and \(5\times 1{0}^{6}\), respectively.