Flat bands and high Chern numbers in twisted multilayer graphene

Abstract

Motivated by recent Physical Review Letters of Wang and Liu [Phys. Rev. Lett. 128(17), 176403 (2022)] and Ledwith, Vishwanath, and Khalaf [Phys. Rev. Lett. 128(17), 176404 (2022)], we study [G. Tarnopolsky, A. Kruchkov, and A. Vishwanath, Phys. Rev. Lett. 122(10), 106405 (2019)] chiral model of two sheets of n-layer Bernal stacked graphene twisted by a small angle using the framework developed by Becker et al. [Probab. Math. Phys. 3(1), 69 (2022)]. We show that magic angles of this model are exactly the same as magic angles of chiral twisted bilayer graphene with multiplicity. For small inter-layer tunneling potentials, we compute the band separation at Dirac points as we turning on the tunneling parameter. Flat band eigenfunctions are also constructed using a new theta function argument and this yields a complex line bundle with the Chern number −n.