Fig. 1. Bott index of TBG quasicrystal with different intensities of t_R. The inset is the atomic structure of TBG quasicrystal. λ = 0.18t₁ and t₂ = 0.12t₁.

Fig. 2. (a) Discrete energy levels of TBG quasicrystal. (b) Bulk LDOS of TBG quasicrystal. The two dashed lines denote the region of bulk gap. The discrete energy levels in bulk gap are the in-gap chiral edge states. The spatial distribution of in-gap chiral edge state at the energy level marked by the blue dot is shown in the inset of (a), which is localized at the boundary of TBG quasicrystal. The circle size denotes the weight of chiral edge state. λ = 0.18t₁, t_R = 0.2t₁, t₂ = 0.12t₁.

Fig. 3. (a) Bulk LDOS with different intensities of t_R. The two dashed lines denote the region of bulk gap. λ = 0.18t₁, t₂ = 0.12t₁. (b) The number of in-gap edge state vs. the system size. The dashed line is a linear fitting of the calculated results. t_R = 0.2t₁.

Fig. 4. (a) Device setup of the TBG quasicrystal ribbon. The square lattice denotes the semi-infinite lead region. (b) Conductance vs. the energy without disorder. (c) and (d) LDOS distribution in the center-scattering region at the energy level marked by the blue dots in (b). (e)–(g) Conductance vs. the energy with on-site-energy, interlayer, and intralayer hopping disorder, respectively. The error bar denotes the fluctuation of conductance among different disorder configurations. λ = 0.18t₁, t_R = 0.2t₁, t₂ = 0.12t₁.