The magic-angle twisted bilayer graphene (MATBG) recently attracted intensive research attention because of its fascinating and unconventional electronic properties. Herein, we claim the magic-angle phenomenon originates from the Heisenberg uncertainty principle, which can provide intensive explanations on finite size effect and twist-dependent low energy band variations. We showed that flat bands could exist only near the AA stacking structure rather than AB. The finite-size effect gives the minimal size of graphene quantum dots (R ≳ 4 nm) for the emergence of the Dirac point, and the uncertainty relation provides the upper bound for moiré supercells (R ≲ 23.5 nm) in twisted bilayer graphene, which is the quantum mechanical boundary for the emergence of flat bands. Combining the twist dependence of moiré supercell size, we proved that there is only one possible magic angle in MATBG at θ ≈ 1.1°. Our result implies that the unconventional phenomena in MATBG originate from the fundamental feature of condensed matter physics.

中文翻译：

---

扭曲双层石墨烯中魔角的起源是海森堡的不确定性原理

魔角扭曲双层石墨烯（MATBG）由于其迷人且非常规的电子特性，最近引起了广泛的研究关注。在这里，我们声称魔角现象源于海森堡不确定性原理，它可以对有限尺寸效应和扭曲相关的低能带变化提供深入的解释。我们表明平坦带只能存在于 AA 堆叠结构附近而不是 AB 附近。有限尺寸效应为狄拉克点的出现给出了石墨烯量子点的最小尺寸（R ≳ 4 nm），不确定性关系提供了莫尔超胞（R≲ 23.5 nm）在扭曲双层石墨烯中，这是平带出现的量子力学边界。结合莫尔超胞尺寸的扭曲依赖性，我们证明了在 θ≈1.1° 的 MATBG 中只有一种可能的魔角。我们的结果意味着 MATBG 中的非常规现象源于凝聚态物理的基本特征。