Title: Degenerate flat bands in twisted bilayer graphene Show Chinese title

Title: 扭转双层石墨烯中的退化平带

Abstract: We prove that in the chiral limit of the Bistritzer--MacDonald Hamiltonian, there exist magic angles at which the Hamiltonian exhibits flat bands of multiplicity four instead of two. We analyse the structure of Bloch functions associated with the bands of arbitrary multiplicity, compute the corresponding Chern number to be $ -1 $, and show that there exist infinitely many degenerate magic angles for a generic choice of tunnelling potential, including the Bistritzer--MacDonald potential. Moreover, we demonstrate for generic tunnelling potentials flat bands have only twofold or fourfold multiplicities. Show Chinese abstract

Abstract: 我们证明了在Bistritzer--MacDonald哈密顿量的手征极限中，存在魔角，在这些魔角处，哈密顿量表现出四重简并的平带，而不是双重简并。我们分析了任意重数带的布洛赫函数结构，计算出对应的陈数为$ -1 $，并且表明对于一般的隧穿势选择（包括Bistritzer--MacDonald势），存在无穷多个退化的魔角。此外，我们证明了对于一般的隧穿势，平带只有二重或四重简并。