标题： 扭曲多层石墨烯中的平带、狄拉克锥和高阶能带交叉 显示英文标题

标题： Flat bands, Dirac cones, and higher-order band crossings in twisted multilayer graphene

摘要： 对于在《物理评论快报》arXiv:2109.10325 和 arXiv:2109.11514 中建立的两层$n$层 Bernal 叠加石墨烯的手性极限，我们证明了一个三重性：根据扭转角度，我们有以下三种情况：(1) 通常情况下，前两个能带的交叉为$n$阶；或者 (2) 在一组离散的魔法角度下，前两个能带完全平坦；或者 (3) 对于另一组离散的扭转参数，能带表现出狄拉克锥。这一新的数学发现推翻了物理学中常见的观点，即这种扭曲多层石墨烯模型只能具有高阶能带交叉或平坦能带，并导致了一种新型的拓扑相变。 显示英文摘要

摘要： For the chiral limit of two sheets of $n$-layer Bernal-stacked graphene established in the Physical Review Letters arXiv:2109.10325 and arXiv:2109.11514, we prove a trichotomy: depending on the twisting angle, we have either (1) generically, the band crossing of the first two bands is of order $n$; or (2) at a discrete set of magic angles, the first two bands are completely flat; or (3) for another discrete set of twisting parameters, the bands exhibit Dirac cones. This new mathematical discovery disproves the common belief in physics that such a twisted multilayer graphene model can only have higher order band crossings or flat bands, and it leads to a new type of topological phase transition.