Fig. 5: DFT magic distance vs twist angle θ.

(Blue circled points) DFT-derived magic distances \({\tilde{d}}_{{\rm{M}}}={\tilde{d}}_{m}\)vs. commensurate twist angles θ = θ_m (bottom horizontal axis) for m = 6, …, 9 (top horizontal axis). (Red circled point) MA condition established at the TB level: d₀ = 3.349 Å and θ₀ = 1.05°. (Red dashed line) Function in Eq. (10), derived using the reference values d₀, θ₀, and the best-fit parameter β_DFT = 1.891 Å⁻¹. (Green dotted line) Function in Eq. (10), with parameters \({\beta }_{{\rm{DFT}}}^{{\prime} }=1.605\) Å⁻¹ and, equivalently, \({\theta }_{0}^{{\prime} }=1.2{9}^{\circ }\) at fixed d₀, or \({d}_{0}^{{\prime} }=3.480\) Å at fixed θ₀. (Black circled point) Interlayer distance \({\tilde{d}}_{5}\) at the twisted angle θ₅, excluded from the fitting processes above.